Dr. Sukumar Das Adhikari

Table of Contents:

General Information:

  • Name: Dr. Sukumar Das Adhikari
  • Designation: Professor and Dean, School of Mathematical Sciences
  • Contact No: (033) 2654-9999
  • Email: ,
  • Home Page: https://maths.rkmvu.ac.in/sukumar-das-adhikari/

Academic Qualification

  • Ph. D. in Mathematics from the Institute of Mathematical Sciences, Madras (Degree awarded by the University of Madras).
    Thesis supervisor : Prof. R. Balasubramanian.

Mathematical Interests :

  • Number Theory and Combinatorics.

Research Papers:

  1. Chessboard Domination: Introduction of some new problems (Written jointly with Shruti Hegde and Md Ibrahim Molla); To appear.
  2. On some weighted zero-sum constants (Written jointly with Shruti Hegde); Journal of the Ramanujan Mathematical Society (JRMS), volume 37, No. 3, 281–286 (2022).
  3. Inverse problems related to some weighted zero-sum constants for cyclic groups (Written jointly with Shruti Hegde, Md Ibrahim Molla and Subha Sarkar); Integers 22 (2022), Paper No. A7.
  4. Zero-sum constants involving weights (Written jointly with Shruti Hegde); Proc. Indian Acad. Sci. (Math. Sci.), volume 131, Article number: 37 (2021).
  5. Extremal sequences for some weighted zero-sum constants for cyclic groups (Written jointly with Md Ibrahim Molla and Shameek Paul); 1–10, Springer Proc. Math. Stat., 347, Springer, Cham, 2020.
  6. On a conjecture of Fox-Kleitman and Additive Combinatorics (Written jointly with R. Balasubramanian, S. Eliahou and D. Grynkiewicz); Proc. Indian Acad. Sci. (Math. Sci.), 129, no. 4, Art. 43, 7 pp. (2019).
  7. Numerical semigroups of Szemer’edi type (Written jointly with L.~Boza, S.~Eliahou, M.~P.~Revuelta and M.~I.~Sanz); Discrete Applied Mathematics, 263, 8–13 (2019).
  8. On the degree of regularity of a particular linear equation (Written jointly with R. Balasubramanian, S. Eliahou and D. Grynkiewicz); Acta Arithmetica, 184, no. 2, 187 — 191 (2018).
  9. On the degree of regularity of a certain quadratic Diophantine equation (Written jointly with L. Boza, S. Eliahou, M. Revuelta and M. Sanz); European J. Combin. Vol. 70, 50–60 (2018).
  10. Equation-regular sets and the Fox-Kleitman conjecture (Written jointly with L. Boza, S. Eliahou, M. Revuelta and M. Sanz); Discrete Mathematics, Vol. 341, 287–298 (2018).
  11. On a conjecture of Fox and Kleitman on the degree of regularity of a certain linear equation (Written jointly with S. Eliahou); Combinatorial and Additive Number Theory II, 1-8, Springer Proc. Math. Stat., 220, Springer, Cham, 2017.
  12. The analog of the ErdH{o}s distance problem in finite fields (Written jointly with Anirban Mukhopadhyay and M. Ram Murty); Int. J. Number Theory , Vol. 13, No. 9, 2319–2333 (2017).
  13. On the finiteness of some $n$-color Rado numbers (Written jointly with L. Boza, S. Eliahou, J. Mar’in, M. Revuelta and M. Sanz); Discrete Mathematics, Vol. 340, 39–45 (2017).
  14. Relation between two weighted zero-sum constants (Written jointly with Eshita Mazumdar and B. K. Moriya); Integers , 16, paper A 20, (2016).
  15. On the $n$-color Rado number for the equation $x_1+x_2+dots +x_k+c =x_{k+1}$ (Written jointly with L. Boza, S. Eliahou, J. Mar’in, M. Revuelta and M. Sanz); Math. Comp., Vol. 85, 2011-2045 (2016).
  16. The polynomial method in the study of zero-sum theorems (Written jointly with Eshita Mazumdar); Int. J. Number Theory, Vol. 11, No. 5, 1451–1461 (2015).
  17. On monochromatic configurations for finite colorings (Written jointly with Yong-Gao Chen); Discrete Mathematics, Vol. 333, 106–109 (2014).
  18. ErdH{o}s-Ginzburg-Ziv theorem for finite commutative semigroups (Written jointly with Weidong Gao and Guoqing Wang); Semigroup Forum, 88, Issue 3, 555–568, (2014).
  19. Modifications of some methods in the study of zero-sum constants (Written jointly with Eshita Mazumdar); Integers , 14, paper A 25, (2014).
  20. Remarks on monochromatic configurations for finite colorings of the plane (Written jointly with Purusottam Rath); Note di Matematica, 32, no. 2, 83 –88 (2012).
  21. On weighted zero-sum sequences (Written jointly with David J. Grynkiewicz and Zhi-Wei Sun); Advances in Applied Mathematics, 48, 506–527, (2012).
  22. Number of weighted subsequence sums with weights in ${1,-1}$} (Written jointly with Mohan N. Chintamani); Integers , 11, paper A 36, (2011).
  23. Zero-sum problems with subgroup weights (Written jointly with A. A. Ambily and B. Sury); Proc. Indian Acad. Sci. (Math. Sci.), 120, No. 3, 259–266 (2010).
  24. Visibility in the plane (Written jointly with Andrew Granville); J. Number Theory , 129, Issue 10, 2335–2345 (2009).
  25. Remarks on some zero-sum theorems (Written jointly with Sanoli Gun and Purusottam Rath); Proc. Indian Acad. Sci. (Math. Sci.), 119, No. 3, 275–281 (2009).
  26. Weighted sums in finite Abelian groups (Written jointly with Mohan N. Chintamani, Bhavin K. Moriya and Prabal Paul); Uniform Distribution Theory, 3, no. 1, 105–110 (2008).
  27. Generalizations of some zero-sum theorems (Written jointly with Chantal David and Jorge Jim’enez Urroz); Integers , 8, paper A 52, (2008).
  28. Some zero-sum constants with weights (Written jointly with R. Balasubramanian, F. Pappalardi and P. Rath); Proc. Indian Acad. Sci. (Math. Sci.), 118, 183 –188 (2008).
  29. Davenport constant with weights and some related questions – II (Written jointly with Y. G. Chen); Journal of Combinatorial Theory, Series A, 115, 178–184 (2008).
  30. Davenport constant with weights and some related questions (Written jointly with P. Rath); Integers , 6, paper A 30, (2006).
  31. Contributions to zero–sum problems (Written jointly with Y. G. Chen, J. B. Friedlander,S. V. Konyagin and F. Pappalardi); Discrete Mathematics, Vol. 306, 1, 1–10 (2006).
  32. On the sets of uniqueness of the distribution function of ${ xi (p/q)^n}$} (Written jointly with P. Rath and N. Saradha); Acta Arithmetica, 119, no. 4, 307 — 316 (2005).
  33. Monochromatic configurations for finite colourings of the plane (Written jointly with Purusottam Rath); Note di Matematica, 22, no. 1, 59 –63 (2003/04).
  34. Remarks on some zero-sum problems. (Written jointly with Purusottam Rath); Expo. Math., 21, no. 2, 185 — 191 (2003).
  35. Remarks on the visibility problem in the function field case. (Written jointly with Francesco Pappalardi); C. R. Math. Acad. Sci. Soc. R. Can., 24 (3), 109–116 (2002).
  36. On a question regarding visibility of lattice points-III. (Written jointly with Yong-Gao Chen); Discrete Mathematics, Vol. 259, 1-3, 251-256 (2003).
  37. Corrigenda To `Further remarks on Steinhaus sets’. (Written jointly with R. Balasubramanian and R. Thangadurai); Publ. Math. Debrecen, 60/ 1-2, 209-210 (2002).
  38. On the average of the sum-of-the $p$- prime-divisors function. (Written jointly with G. Coppola and Anirban Mukhopadhyay); Acta Arith. 101, no. 4, 333 — 338 (2002).
  39. On the average of sum-of-odd-divisors function. (Written jointly with G. Coppola); Current Trends in Number Theory (proceedings of the international conf. held at HRI in November 2000), 1–15, Hindustan Book Agency, New Delhi, 2002.
  40. On a theorem of Graham; Expo. Math. 19, no. 4, 365 — 367 (2001).
  41. Transcendental infinite sums. (Written jointly with N. Saradha, T.N.Shorey and R. Tijdeman); Indag. Math. (N.S.), 12 (1) 1–14 (2001).
  42. Further Remarks on Steinhaus sets. (Written jointly with R. Balasubramanian and R. Thangadurai); Publ. Math. Debrecen 57/ 3-4. 277-281 (2000)
  43. Monochromatic solutions of Diophantine equations. (Written jointly with R. Thangadurai); Algebraic Number Theory and Diophantine Analysis (Graz., 1998) 1–9 de Gruyter, Berlin, 2000.
  44. On a question regarding visibility of lattice points-II. (Written jointly with Yong-Gao Chen); Acta Arithmetica 89 (1999) no. 3, (279-282)
  45. A note on sets having the Steinhaus property. (Written jointly with R. Thangadurai); Note Mat. 16 (1996), No.1, 77-80 (1998)
  46. A note on a question of Erd”os. Exposition. Math.15, no. 4, 367-371(1997).
  47. Addendum to “A note on the distribution of values of an arithmetical function”. (Written jointly with R. Thangadurai); Indian J. Pure Appl. Math. 28 (1), 125-127, (1997)
  48. On a question regarding visibility of lattice points. (Written jointly with R. Balasubramanian); Mathematika 43, 155-158, (1996).
  49. A note on the distribution of values of an arithmetical function. (Written jointly with R. Thangadurai); Indian J. Pure Appl. Math. 26 (10), 931-935, (1995).
  50. On the average behaviour of an arithmetical function. (Written jointly with K. Chakraborty); Arch. Math. 62, 411-417 (1994).
  51. Towards the exact nature of a certain error term -II. (Written jointly with K. Soundararajan); Arch. Math. 59, 442-449 (1992).
  52. Towards the exact nature of a certain error term. Arch. Math. 58, 257-264 (1992).
  53. Lattice points in ellipsoids. (Written jointly with Y. -F. S. P’etermann); Acta Arithmetica 59, no. 4, 329-338 (1991)
  54. $Omega$- results for sums of Fourier coefficients of cusp forms. Acta Arithmetica 57, no. 2, 83-92 (1991)
  55. A note on a certain error term. (Written jointly with R. Balasubramanian); Arch. Math. 56, 37-40 (1991).
  56. On an error term related to the Jordan totient function $J_k(n)$. (Written jointly with A. Sankaranarayanan); J. Number Theory 34, no 2., 178-188 (1990).
  57. An $Omega$- result related to $r_4(n)$. (with R. Balasubramanian and A. Sankaranarayanan); Hardy – Ramanujan Journal 12, 20-30 (1989).
  58. On an error term related to the greatest divisor of $n$, which is prime to $k$. (Written jointly with R. Balasubramanian and A. Sankaranarayanan); Indian J. Pure Appl. Math. (9) 19, 830-841 (1988).

Expository Articles:

  1. Some zero-sum constants and their weighted generalizations
    (based on the technical talk given as the president of the IMS, in the 88th Annual Conference of the IMS – An International Meet held at BIT, Mesra, Ranchi, Jharkhand during December 27–30, 2022.)
    Math. Student, volume 92, no.1-2, 13–25 (2023).
  2. Discrete stories: stray facts related to some early Ramsey-type theorems
    Math. Student, volume 92, no.1-2, 9–12 (2023).
  3. On a polynomial method of Rónyai in the study of zero-sum theorems
    (Written jointly with Bidisha Roy and Subha Sarkar)
    Modular forms and related topics in number theory, 7–17, Springer Proc. Math. Stat., 340, Springer, Singapore, (2020).
  4. Weighted zero-sums for some finite abelian groups of higher ranks
    (Written jointly with Bidisha Roy and Subha Sarkar)
    Combinatorial and additive number theory. III, 1–12, Springer Proc. Math. Stat., 297, Springer, Cham, (2020).
  5. Plus-minus weighted zero-sum constants: A survey
    Analytic Number Theory, Modular Forms and $q$-Hypergeometric Series, 1-9, Springer Proc. Math. Stat., 221, Springer, Cham, 2017.
  6. Some omega results and related questions connected to R. Balasubramanian’s mathematical work
    (Jointly with D. S. Ramana)
    Highly Composite: Papers in Number Theory, (Eds. V. Kumar Murty and R. Thangadurai), 1–11, Ramanujan Mathematical Society Lecture Notes Series, Number 23, 2016.
  7. An extremal problem in combinatorial number theory
    Proceedings of an International Conference in Celebration of the 125th Anniversary of Ramanujan’s Birth; University of Delhi, 17-22 December 2012, (Eds. Bruce C. Berndt and Dipendra Prasad), 1–11, Ramanujan Mathematical Society Lecture Notes Series, Number 20, 2013.
  8. Schur’s theorem in combinatorial number theory: Some generalizations
    J. Indian Math. Soc. (N.S.) 2013, Special Volume to commemorate the 125th birth anniversary of Srinivasa Ramanujan, 1–10.
  9. ErdH{o}s, Ginzburg and Ziv Theorem: various proofs and some generalizations
    (jointly with Eshita Mazumdar and Sneh Bala Sinha)
    Proceedings of the 21st Annual Conference of the Jammu Mathematical Society, (Eds. K. S. Charak, R. Kumar), 41–48, University of Jammu.
  10. Simplices with monochromatic vertices: Reflections on some problems in Euclidean Ramsey Theory
    (jointly with Purusottam Rath)
    Number Theory, Proceedings in honour of Professor T. C. Vasudevan on his sixtieth birthday, (Eds. M. Manickam and B. Ramakrishnan), 1–5, Ramanujan Mathematical Society Lecture Notes Series, Number 15, 2011.
  11. The Cauchy-Davenport theorem: various proofs and some early generalizations
    (jointly with M. N. Chintamani, Geeta and B. K. Moriya)
    Math. Student, Vol. 79, 109– 116 (2010).
  12. Some omega results and related questions in the research work of Pillai
    (An article about S. S. Pillai’s work)
    Collected works of S. Sivasankaranarayana Pillai (Eds. R. Balasubramanian and R. Thangadurai), l–lvi, Published by Ramanujan Mathematical Society, India, 2010.
  13. The relation between two combinatorial group invariants : History and ramifications
    (Text of the Nineteenth Hansaraj Gupta Memorial Award Lecture at the IMS Conference 2008)
    Math. Student, Vol. 77, 131– 143 (2008).
  14. A pearl of Number Theory, the theorem of van der Waerden
    Mathematics Newsletter, Published by Ramanujan Mathematical Society, Vol. 18, No 2, 58–62, 2008.
  15. A problem on the fractional parts of the powers of $3/2$ and related questions
    (jointly with Purusottam Rath)
    Number Theory and Discrete Geometry, Proceedings of the International Conference on Number Theory & Discrete Geometry held in honour of Professor R. P. Bambah, held at Department of Mathematics, Panjab University (Chandigarh, November 30-December 3, 2005) (Eds. R. Balasubramanian, S. G. Dani, P. M. Gruber and R. J. Hans-Gill), 1–12, Ramanujan Mathematical Society Lecture Notes Series, Number 6, 2008.
  16. An extremal problem in lattice point combinatorics
    (jointly with Stephan Baier and Purusottam Rath)
    Diophantine Equations, (N. Saradha Ed.) 19 –32, Tata Institute of Fundamental Research, Publisher: Narosa, New Delhi, 2008 .
  17. Some combinatorial group invariants and their generalizations with weights
    (jointly with R. Balasubramanian and P. Rath)
    Additive Combinatorics (Eds. Granville, Nathanson, Solymosi) 327 –335, CRM Proceedings and Lecture Notes, Volume 43, American Mathematical Society, 2007.
  18. Zero-sum problems in combinatorial number theory
    (Jointly with P. Rath)
    The Riemann Zeta Function and Related Themes: Papers in Honour of Professor K. Ramachandra, Proceedings of international conf. held at National Institute of Advanced Studies, Bangalore, 13-15 December 2003 (Eds. R. Balasubramanian and K. Srinivas), Ramanujan Mathematical Society Lecture Notes Series, Number 2, 2006.
  19. Some questions regarding visibility of integer lattice points in $I!R^d$}
    Proceedings of the Session in analytic number theory and Diophantine equations (Bonn, January — June 2002) (Eds. D. R. Heath-Brown and B. Z. Moroz), Bonner Mathematische Schriften, {bf Nr. 360}.
  20. Siegel’s Theorem: Finiteness of integral points
    (Jointly with D. S. Ramana)
    Elliptic Curves, Modular Forms and Cryptography, Proceedings of the advanced instructional workshop on Algebraic Number Theory, HRI, Allahabad, 2000 (Eds. A. K. Bhandari, D. S. Nagaraj, B. Ramakrishnan, T. N. Venkataramana), Hindustan Book Agency, New Delhi 2003.
  21. Arithmetic nature of sums of certain convergent series.
    (Jointly with N. Saradha)
    Resonance , Vol. 7, No. 11, 35 — 46, 2002.
  22. Transcendental infinite sums and some related questions.
    Number Theory and Discrete Mathematics (proceedings of international conf. on number theory held at Chandigarh in October 2000), 169– 178, Hindustan Book Agency, New Delhi, 2002.
  23. Partition function congruences: Some flowers and seeds from Ramanujan’s garden.
    (Written jointly with Anirban Mukhopadhyay)
    Expo. Math. Vol. 19, 193– 211 (2001).
  24. The Early Reciprocity Laws: From Gauss to Eisenstein.
    Cyclotomic Fields and Related Topics. edited by S. D. Adhikari, S. A. Katre and Dinesh Thakur, Published by Bhaskaracharya Pratishthana, Pune, 55-74 (2000).
  25. A Problem of Steinhaus concerning the existence of a plane set with a certain property.
    Number Theory and its Applications (Kyoto, 1997) 1-5 Dev. Math.,2, Kluwer Acad. Publ., 1999.
  26. On some questions related to integer lattice points on the plane.
    Number Theory and Applications (Japanese) (Kyoto 1997) S=urikaisekikenky=usho K=oky=uroku No. 1060, (1998), 231-237
  27. The average behaviour of the number of solutions of a Diophantine equation and an averaging technique.
    Number Theory: Diophantine, Computational and Algebraic Aspects, Proceedings of the International Conference held at Eger, Hungary, (Eds. K Gy”ory, A. Peth”o and V. T. S’os), Walter de Gruyter GambH & Co., Berlin, New York, 1–8 (1998).
  28. Lattice points in spheres.
    Bulletin of the Allahabad Mathematical Society, Vol. 8-9, (1993-94), 1– 13 (1997).
  29. Colours in the fields coming in handy: a walk in the garden of Ramsey-type theorems.
    Bona Mathematica, Vol. 6, No 4, 7– 14 (1995).

Invited Talks:

  1. Gave an invited `Special Talk’ at IISER Kolkata on the 25th of February 2025.
  2. Gave an invited talk on 7th February, 2025, at the “National Conference on the Recent Developments in Mathematical Sciences” (NCRDMS-2025) held at School of Mathematics and Statistics, University of Hyderabad, from February 05th to 07th, 2025.
  3. Gave an invited talk on 5th February, 2025, in the International Conference on Pure Mathematics and its Applications (ICPMA-2025), held during 5-7 February, 2025 at the department of Pure Mathematics,
    University of Calcutta, Kolkata.
  4. Gave an invited talk at the International Conference `RECENT ADVANCES IN MATHEMATICS AND RELATED AREAS’ held at SRM University, AP, during JANUARY 14 – 19, 2025.
  5. Gave an invited talk at Ramanujan Institute for Advanced Study in Mathematics, University of Madras, Chennai, on the 137th National Mathematics Day, December 20, 2024.
  6. Gave an invited talk at the International Conference on Number Theory and Related Topics (ICNTRT) held at IMSc, Chennai, from 16th to 18th December 2024.
  7. Gave an invited talk in the conference “Celebrating Number Theory in India”, a conference to celebrate the 70th birthday of Professor M. Ram Murty, held at IISER, Pune, from December 09 – 13, 2024.
  8. Visited the research group Geometric, Algebraic and Probabilistic Combinatorics at UPC, Barcelona (Nov 24-30, 2024), Worked on some research problems and gave a talk there.

Reminiscences, history and biography:

  1. Professor Satya Deo as I knew him Math. Student, volume 92, no.1-2, 5–7 (2023).
  2. Reminiscences of Professor C. S. Seshadri Math. Newsl. volume 31, no. 3, 117 (2020/21).

Monographs/books:

  1. Aspects of Combinatorics and Combinatorial Number Theory. Narosa Publishing House, (2002).
  2. An introduction to Commutative Algebra and Number Theory. Narosa Publishing House, (1999).

Volumes edited:

  1. Number Theory and Applications (proceedings of the international conferences on Number Theory and Cryptography). (Edited jointly with B. Ramakrishnan) Hindustan Book Agency, New Delhi, 2009.
  2. Number Theory (proceedings of the international conf. held at The Institute of Mathematical Sciences, Chennai, in January 2002). (Edited jointly with R. Balasubramanian and K. Srinivas) Ramanujan Mathematical Society Lecture Notes Series, Number 1, 2005.
  3. Current Trends in Number Theory (proceedings of the international conf. held at HRI in November 2000). (Edited jointly with S. A. Katre and B. Ramakrishnan) Hindustan Book Agency, New Delhi, 2002.
  4. Cyclotomic Fields and Related Topics. (Edited jointly with S. A. Katre and Dinesh Thakur), Published by Bhaskaracharya Pratishthana, Pune, 2000.
  5. Current Trends in Mathematics and Physics. A tribute to Harish-Chandra. Narosa Publishing House, New Delhi, 1995.

PhD work supervised:

  1. Dr. R. Thangadurai
  2. Dr. Anirban Mukhopadhyay
  3. Dr. Purusottam Rath
  4. Dr. Anupama Panigrahi
  5. Dr. Bhavin. K. Moriya
  6. Dr. Mohan Chintamani
  7. Dr. Eshita Mazumdar
  8. Dr. Sneh Bala Sinha
  9. Dr. Md Ibrahim Molla
  10. Dr. Shruti Hegde

Other experiences and recognitions:

  1. A fellow of the National Academy of Sciences, India.
  2. Delivered the Nineteenth `Hansraj Gupta Memorial Award Lecture’ of Indian Mathematical Society in 2008.
  3. Received the M K Singhal Memorial Award for the year 2013-14 by the Indian Science Congress Association.
  4. Received Distinguished Faculty Award of Homi Bhabha National Institute (HBNI) in 2015.
  5. Received D. Sc. (Honoris Causa) from Kazi Nazrul University, Asansol, West Bengal, India, in 2016.
  6. Was a member of National Board of Higher Mathematics (NBHM), India (2011-2022).
  7. Was president of the Indian mathematical Society (2022–2023).
  8. A member of the editorial board of `The Journal of the Indian Mathematical Society’.
  9. Had been a member of the editorial board of `Proc. Indian Acad. Sci. (Math. Sci.)’
  10. Was a member of the editorial board of the periodical `Mathematics Newsletter’ published by Ramanujan Mathematical Society.