- Algebraic Number Theory
- Automorphic forms
- Elliptic curve cryptography

Experience top of the world living and learning at SRM University-AP

**+91-863-2343000 080-6988-6999**

Email: admissions@srmap.edu.in

SRM University, Andhra Pradesh

Neerukonda, Mangalagiri Mandal, Guntur District, Mangalagiri, Andhra Pradesh 522240

- Algebraic Number Theory
- Automorphic forms
- Elliptic curve cryptography

- 1997-1998-PDF-IMSc, Chennai
- 1998-2000-PDF-Queen’s University
- 2000-2001-PDF-HRI, Prayagraj, India
- 2001-2024 (May)-Professor-HRI, Prayagraj, India
- 2020 (Aug)--2023(Aug)-Director-Kerala School of Mathematics, India

- 1.
**Class number of number fields:** - (i) Class numbers of number fields are mysterious objects and not much is known about these numbers. One of the many questions is to show the existence of infinitely many number fields (for quadratic field cases many results are known!) whose class number is divisible by a given integer. Quantifying these fields is also an interesting problem. The Cohen-Lenstra heuristics related to these questions is yet to be established. In the direction of indivisibility not much is known though. It's worth looking into these directions relating the arithmetic of some kind of modular forms and that of elliptic curves.
- (ii) There are few well known conjectures (e.g. Vandiver conjecture) relating to the class number of maximal real subfields of cyclotomic fields. The above problems of divisibility and indivisibility are worth exploring here in this set up. This will give us information about the class numbers of the corresponding cyclotomic fields too. These numbers are not easy to calculate by using the class number formula.
**2. Modular relations:**- (i) Consider applications of the theory of zeta-functions to ‘Theoretical Computer Science’. We begin by studying the work of Anshell and Goldfeld in which they add one more condition on the coefficients of the Euler product, i.e. polynomial time evaluation algorithm for the values at prime powers. Then we study the work of Kirschenhoffer and Prodinger about the trie algorithm. In contrast to Knuth’s work, they deduce the exact formula for the expectation and for the variance they used Ramanujan’s formulas for the Riemann zeta-values involving Lambert series. We believe there must be a disguised form of the modular relation.
- (ii) Study Mertens’ formula for a class of zeta-functions as we have studied in one of our previous work. We also reveal the hidden structure of Vinogradov’s work on a general Mertens’ formula in number fields.
**3. Chow groups, class groups and Tate-Shafarevich groups:**- Aimed at studying the inter-relations between these three important groups. In particular it aims at transferring certain properties of one group to the other.

- 2021- Fellow of West Bengal Academy of Science and Technology- West Bengal Academy of Science and Technology
- 2024-Ganesh Prasad Memorial Award-Indian Mathematical Society

- Working as a vice-president of Society for Special Functions and Applications (SSFA)
- Set up the Mathematics Department at Tribhuvan University, Nepal
- Organized some INSPIRE camp.
- Organized 6 international conferences under the name ‘ICCGNFRT’.

- 1. Kalyan Chakraborty, Shubham Gupta and Azizul Hoque, Diophantine $D(n)$-quadruples in $mathbb{Z}[sqrt{4k+2}]$, Glasnik Matematicki (to appear)
- 2. Kalyan Chakraborty, and Azizul Hoque, On the plus parts of the class numbers of cyclotomic fields, Chinese Annals of Mathematics, Series B (to appear)
- 3. Kalyan Chakraborty and Azizul Hoque, Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields, The Ramanujan Journal, 60 (2023), no. 4, 913--923.
- 4. Kalyan Chakraborty, and Azizul Hoque, On the exponential Diophantine equation $x^2+p^mq^n=2y^p$, New Zealand Journal of Mathematics (to appear).
- 5. Om Prakash and Kalyan Chakraborty, Generalized fruit diophantine equation and hyperelliptic curves, Volume 203, 667–676, (2024)
- 6. Kalyan Chakraborty, Shubham Gupta and Azizul Hoque, Diophantine triples with the property $D(n)$ for distinct $n$'s, Mediterranean Journal of Mathematics, 20 (2023), no. 1, 13pp, article no. 31. arXiv: 2204.14208
- 7. Kalyan Chakraborty, Shubham Gupta and Azizul Hoque, On a conjecture of Franuvsi'c and Jadrijevi'c: Counter-examples, Results in Mathematics, 78 (2023), no. 1, 14pp, article no. 18.
- 8. Kalyan Chakraborty, and Azizul Hoque, On the Diophantine equation $dx^2+p^{2a}q^{2b}=4y^p$, Results in Mathematics, 77 (2022), no. 1, 11pp, article no. 18.
- 9. Kalyan Chakraborty and Krishnarjun Krishnamoorthy, On some symmetries of the base n expansion of 1∕m : the class number connection, 319 (2022), No. 1, 39–53
- 10. K. Chakraborty, S. Kenmitsu and A. Laurinčikas, Complex powers of L-functions and integers without large prime factors, Mediterr. J. Math. (2022) 19:167
- 11. Kalyan Chakraborty, Richa Sharma, On a family of elliptic curves of rank at least 2, Czechoslovak Mathematical Journal 72 (2022), no. 3, 1-13.
- 12. Rishabh Agnihotri, Kalyan Chakraborty and Krishnarjun Krishnamoorthy, Sign changes in restricted coefficients of Hilbert modular forms, 59, pages 1225–1243, (2022)
- 13. Rishabh Agnihotri, Kalyan Chakraborty, On the Fourier coefficients of certain Hilbert modular forms, 58, pages 167–182, (2022)
- 14. Chiranjit Ray and Kalyan Chakraborty, Certain eta-quotients and $$ell $$-regular overpartitions, 57, pages 453–470, (2022)
- 15. Kalyan Chakraborty and Krishnarjun Krishnamoorthy, On Moments of non-normal number fields, Journal of number theory, 238 (2022), 183-196
- 16. On the solutions of certain Lebesgue-Ramanujan-Nagell equations (with Kalyan Chakraborty, Richa Sharma), Rocky Mountain Journal of Mathematics, 51 (2021), no. 2, 459--471.
- 17. On the Diophantine equation $cx^2+p^{2m}=4y^n$ (with Kalyan Chakraborty, Kotyada Srinivas), Results in Mathematics, 76 (2021), no. 2, 12pp, article no. 57. arXiv: 2102.07977
- 18. An analogue of Wilton's formula and values of Dedekind zeta functions (with Soumyarup Banerjee, Kalyan Chakraborty), Journal of Mathematical Analysis and Applications, 495 (2021), no. 1, 20pp, 124675.arXiv:1611.08693
- 19. Kalyan Chakraborty and Takao Komatsu, Generalized hypergeometric Bernoulli numbers, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 115, article number 101, (2021)
- 20. Rishabh Agnihotri, Kalyan Chakraborty, Sign changes of certain arithmetical function at prime powers, Czechoslovak Mathematical Journal 71(4):1221-1228
- 21. On the structure of order 4 class groups of $mathbb{Q}(sqrt{n^2+1})$ (with Kalyan Chakraborty, Mohit Mishra), Annales Math'ematiques du Qu'ebec, 45 (2021), no. 1, 203--212. arxiv:1902.05250
- 22. Exponents of class groups of certain imaginary quadratic fields (with Kalyan Chakraborty), Czechoslovak Mathematical Journal, 70 (2020), no. 4, 1167--1178. arXiv:1801.00392
- 23. Complete solutions of certain Lebesgue-Ramanujan-Nagell type equations (with Kalyan Chakraborty, Richa Sharma), Publicationes Mathematicae Debrecen, 97 (2020), no. 3-4, 339--352. arXiv:1812.11874
- 24. A note on certain real quadratic fields with class number upto three (with Kalyan Chakraborty, Mohit Mishra), Kyushu Journal of Mathematics, 74 (2020), no. 1, 201--210.
- 25. Mohit Mishra, Rishabh Agnihotri and Kalyan Chakraborty, Primary rank of the class group of real cyclotomic fields, Rocky Mountain J. Math. 50 (2020) (6): 2149-2155.
- 26. Kalyan Chakraborty ; Chiranjit Ray, Distribution of generalized mex-related integer partitions, Hardy-Ramanujan Journal, 43, 2020, 122-128
- 27. Divisibility of Selmer groups and class groups (with Kalyan Banerjee, Kalyan Chakraborty), Hardy-Ramanujan Journal, 42 (2019), 85--99. arXiv: 1912.02420
- 28. Divisibility of class numbers of certain families of quadratic fields (with Kalyan Chakraborty), Journal of the Ramanujan Mathematical Society, 34 (2019), no. 3, 281--289.
- 29. Banerjee, S. and Chakraborty, K. Asymptotic behaviour of a Lambert series á La Zagier: Maass case, Ramanujan J., Vol. 48 (2019), no. 3, 567–575.
- 30. K. Chakraborty and A. Hoque, Class groups of imaginary quadratic fields of 3 - rank at least 2, Annales UMCS Mathematica Vol. 47(2018), 179–183.
- 31. K. Chakraborty, S. Kanemitsu and T. Kuzumaki, Seeing the invisible: Kubert identities, Annales UMCS Vol 47 (2018), 185–195.
- 32. K. Chakraborty, A. Juyal, S. D. Kumar and B. Maji, Asymptotic expansion of a Lambert series associated to cusp forms, Int. J. Number Theory , Vol.14 (2018), No. 1, 289–299. https://doi.org/10.1142/S1793042118500173
- 33. K. Chakraborty, A. Hoque, Y. Kishi and P. P. Pandey, Divisibility of class numbers of imaginary quadratic fields, J. Number Theory, Vol. 185 (2018), pp. 339–348. DOI: 10.1016/j.jnt.2017.09.007.
- 34. Chakraborty, K. and Hoque, A. Pell-type equations and class number of the maximal real subfield of a cyclotomic field, Ramanujan J (2018), DOI: 10.1007/s11139- 017-9963-9.
- 35. K. Chakraborty, J. J. Urroz and Francesco Pappalardi, Pairs of integers which are mutually squares, Sci China Math, Vol. 60 (2017), 1633–1646.
- 36. D. Banerjee, K. Chakraborty , S. Kanemitsu and B. Maji, Abel-Tauber process and asymptotic formulas, Kyushu J. Math. Vol. 71 (2017), Issue 2, pp. 363-385 DOI https://doi.org/10.2206/kyushujm.71.363
- 37. K. Chakraborty, S. Kanemitsu and H. Tsukada, Ewald expansions of a class of zeta-functions, SpringerPlus, 2016, 5:99, DOI 10.1186/s40064-016-1732-5.
- 38. K. Chakraborty and S. Kanemitsu and B. Maji, Modular type relations associated to the Rankin-Selberg L-functions, Ramanujan J. , Vol. 42 (2017), Issue 2, pp. 285–289. doi:10.1007/s11139-015-9759-8
- 39. K. Chakraborty, I. Kátai and B. M. Phong, Additive functions on the greedy and lazy Fibonacci expansions, J. Integer Seq. 19 (2016), no. 4, 16.4.5, pp. 12 .
- 40. K. Chakraborty, S. Kanemitsu and H. -L. Li, Quadratic reciprocity and Riemann’s non-differentiable function, Res. Number Theory No. 1(2015) 1:14, DOI 10.1007/s40993-015-5.
- 41. K. Chakraborty and M. Minamide, On power moments of the Hecke multiplica- tive functions, J. Aust. Math. Soc., Vol. 99 (2015), 334–340. 2015), doi: 10.1017/S1446788715000063.
- 42. T. Arai, K. Chakraborty and S. Kanemitsu, On Modular Relations, Number theory, Ser. Number Theory Appl., No. 11, World Sci. Publ., Hackensack, NJ, (2015), 1–64.
- 43. Kalyan Chakraborty and Jay Mehta, Preventing unknown key-share attack using cryptographic bilinear maps, J. Discrete Math. Sci. and Crypt., Vol. 17 (2014), No. 2, 135–147.
- 44. K. Chakraborty and M. Minamide, On partial sums of a spectral analogue of the Möbius function, Proc. Indian Acad. Sci. (Math. Sci.), Vol.123, No. 2 (2013), 193–201.
- 45. K. Chakraborty, S. Kanemitsu and T. Kuzumaki, On The Class Number Formula of Certain Real Quadratic Fields, Hardy-Ramanujan J., Vol. 36 (2013), 1–7.
- 46. K. Chakraborty, I. Kátai and B. M. Phong, On additive functions satisfying some relations, Ann. Univ. Sci. Budapest., Sect. Comput., Vol. 38 (2012), 1–12.
- 47. K. Chakraborty, I. Kátai and B M Phong, On the values of arithmetic functions in short intervals, Ann. Univ. Sci. Budapest., Sect. Comput., Vol. 38 (2012), 13–21.
- 48. K. Chakraborty, S. Kanemitsu and H. Tsukada, Arithmetical Fourier series and the modular relation, Kyushu J. Math., Vol. 66, No. 2 (2012), 411–427.
- 49. K. Chakraborty, I. Kátai and B.M. Phong, On real valued additive functions modulo 1, Ann. Univ. Sci. Budapest., Sect. Comput., Vol. 36 (2012), 355–373.
- 50. K. Chakraborty and J. Mehta, A stamped blind signature scheme based on elliptic curve discrete logarithm problem, International J. Network Security, Vol. 14, No. 6 (2012), 316–319.
- 51. K. Chakraborty and J. Mehta, On completely multiplicative complex valued func- tions, Ann. Univ. Sci. Budapest, Sect. Comput., Vol. 38 (2012), 19–24.
- 52. K. Chakraborty, S. Kanemitsu and X. -H. Wang, The modular relation and the digamma function, Kyushu J. Math., Vol. 65 (2011), No. 1, 39–53.
- 53. K. Chakraborty, S. Kanemitsu and H.-L. Li On the value of a class of Dirichlet series at rational arguments, Proc. Amer. Math. Soc., Vol. 138 (2010), 1223–1230.
- 54. K. Chakraborty, On the Chowla-Selberg integral formula for non-holomorphic Eisen- stein series, Integral Transforms and Special Functions, Vol. 21, No. 12, Dec. 2010, 917–923 (7).
- 55. K. Chakraborty, F. Luca, Perfect powers in solutions to Pell equations, Revista Columbiana de Matematicas, Vol. 43 (2009), 71–86.
- 56. K. Chakraborty, S. Kanemitsu and J. -H. Li Manifestations of the Parseval identity, Proc. Japan Acad., Vol. 85, Ser. A, 9 (2009), 149–154.
- 57. K. Chakraborty, S. Kanemitsu and T. Kuzumaki, Finite expressions for higher derivatives of the Dirichlet L - function and the Deninger R - function, Hardy- Ramanujan J., Vol. 32 (2009) 38–53.
- 58. K. Chakraborty, F. Luca, A. Mukhopadhyay, Exponents of class groups of real quadratic fields, Int. J. Number Theory, Vol.4 (2008), 1–15.
- 59. K. Chakraborty, F. Luca and A. Mukhopadhyay, Real quadratic fields with class numbers having many distinct prime factors, J. Number Theory, Vol.128 (2008), No. 9, 2559–2572.
- 60. K. Chakraborty, On the Diophantine equation x + y + z = xyz = 1, Ann. Univ. Sci. Budapest. Sect. Comput., Vol. 27 (2007).
- 61. Kalyan Chakraborty and A. Mukhopadhyay, Exponents of class groups of real quadratic function fields (II), Proc. Amer. Math. Soc., Vol. 134 (2006), No. 1, 51–54
- 62. K. Chakraborty and Anirban Mukhopadhyay, Exponents of class groups of real quadratic function fields, Proc. Amer. Math. Soc., Vol. 132 (2004), No. 7, 1951–1955.
- 63. Kalyan Chakraborty, On the divisibility of class numbers of real quadratic Fields, RIMS Conference Proceedings, Kyoto Univ., (2004).
- 64. K. Chakraborty and M. Ram Murty, On the number of real quadratic fields with class number divisible by 3, Proc. Amer. Math. Soc., Vol. 131 (2003), No. 1, 41–44.
- 65. S. Baba, K. Chakraborty and Y. N. Petridis, On the number of Fourier coefficients that determine a Hilbert modular form, Proc. Amer. Math. Soc., Vol. 130 (2002), No. 9, 2497–2502.
- 66. K. Chakraborty and M. V. Kulkarni, Solutions of cubic equations in quadratic fields, Acta Arithmetica, Vol. LXXXIX.1 (1999) 37–43.
- 67. K. Chakraborty, A. K. Lal and B. Ramakrishnan, Modular forms which behave like theta series, Mathematics of Computation, Vol. 66 (1997), 1169–1183.
- 68. K. Chakraborty, B. Ramakrishnan and T. C. Vasudevan, A Note on Jacobi forms of Higher degree, Abh. Math. Sem. Univ. Hamburg, Vol. 65 (1995), 89–93.
- 69. K. Chakraborty and B. Ramakrishnan, A note on Hecke Eigen forms, Arch. Math., Vol. 63 (1994), 509–517.
- 70. S. D. Adhikari and K. Chakraborty, On the average behaviour of an arithmetical function, Arch. Math., Vol. 62 (1994), 411–417.

**(B) Books/edited volumes**

- 1. Kalyan Chakraborty, Azizul Hoque and Prem Prakash Pandey, Class groups of Number Fields and Related Topics, II , Springer, 2024. (to appear).
- 2. Sandeep Singh Chahal, Kalyan Chakraborty, Baljinder Kour and Sandeep Kaur, Topics in Algebra, Analysis and Topology, CRC press, 2024 (to appear).
- 3. Pradip Debnath, Hari Mohan Srivastava, Kalyan Chakraborty and Poom Kumam, Advances in Number Theory and Applied Analysis, World Scientific, 2022 (edited).
- 4. Kalyan Chakraborty, Azizul Hoque and Prem Prakash Pandey, Class groups of Number Fields and Related Topics, Springer, 2019. (Edited).
- 5. Kalyan Chakraborty, Shigeru Kanemitsu and Takako Kuzumaki, A Quick Introduc- tion to Complex Analysis, World Scientific, Singapore, 2016.
- 6. Kalyan Chakraborty, Shigeru Kanemitsu and Haruo Tsukada, Vistas of Special Functions II, World Scientific, Singapore, 2009.

**E-mail id: kalyan.c@srmap.edu.in**