PUBLICATIONS

Journal Publications

  1. S. D. Adhikari and K. Chakraborty, On the average behaviour of an arithmetical function, Arch. Math., vol.62, (1994), 411-417.
  2. K. Chakraborty and B. Ramakrishnan, A note on Hecke eigen forms, Arch. Math., vol. 63, (1994), 509-517.
  3. 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.
  4. K. Chakraborty, A. K. Lal and B. Ramakrishnan, Modular forms which behave like theta series, Mathematics of Computation, Vol.66 (1997), 1169-1183.
  5. K. Chakraborty and Manisha V. Kulkarni, Solutions of cubic equations in quadratic elds, Acta arithmetica, Vol.LXXXIX.1 (1999) 37-43.
  6. Srinath Baba, K. Chakraborty and Yiannis N. Petridis, On the number of Fourier coecients that determine a Hilbert modular form, Proc. Amer. Math. Soc., Vol.130 (2002), No. 9, 2497-2502.
  7. K. Chakraborty and M. Ram Murty, On the number of real quadratic elds with class number divisible by 3, Proc. Amer. Math. Soc., Vol.131 (2003), No. 1, 41-44.
  8. Kalyan Chakraborty and Anirban Mukhopadyay, Exponents of class groups of real quadratic function elds, Proc. Amer. Math. Soc., Vol.132 (2004), No. 7, 1951-1955.
  9. Kalyan Chakraborty and Anirban Mukhopadyay, Exponents of class groups of real quadratic function elds (II), Proc. Amer. Math. Soc., Vol.134 (2006), No. 1, 51-54.
  10. Kalyan Chakraborty, On the Diophantine equation x+y+z = xyz = 1, Annales Univ. Sci. Budapest. Sect. Comp., 27 (2007).
  11. Kalyan Chakraborty, Florian Luca, Anirban Mukhopadyay, Exponents of class groups of real quadratic elds, International Journal of Number Theory, Vol.4 (2008), 1-15.
  12. Kalyan Chakraborty, Florian Luca and Anirban Mukhopadyay, Real quadratic elds with class numbers having many distinct prime factors, J. Number Theory 128(2008), No. 9, 2559-2572.
  13. Kalyan Chakraborty, Florian Luca, Perfect powers in solutions to Pell equations, Revista Columbiana de Matematicas, Vol. 43 (2009)1, 71- 86.
  14. K. Chakraborty, S. Kanemitsu and J. -H. Li Manifestations of the Parseval identity, Proc. Japan Acad. 85, Ser. A, 9 (2009), 149-154.
  15. K. Chakraborty, S. Kanemitsu, H. Kumagai and Y. Kubara, Shapes of objects and the golden ratio, Journal Of Sangluo University, Vol. 23, No. 4, 2009, 18-27.
  16. K. Chakraborty, S. Kanemitsu and T. Kuzumaki, Finite expressions for higher derivatives of the Dirichlet L - function and the Deninger R - function, Hardy-Ramanujan Journal, Vol. 32, (2009) 38-53.

Recent Publications (2010 Onwards)

  1. K. Chakraborty, S. Kanemitsu and H.-L. Li On the value of a class of Dirichlet series at rational arguments, Proc. Amer. Math. Soc. 138 (2010), 1223{1230.
  2. K. Chakraborty, On the Chowla-Selberg integral formula for non-holomorphic Eisenstein series, Integral Transforms and Special Functions, Vol. 21, No. 12, Dec. 2010, 917-923 (7).
  3. K. Chakraborty, S. Kanemitsu, Y. Katayama and Y. Nitta, Sustainibility of ancient constructions and non-associated numbers, Journal of Sangluo University, Vol. 24, No. 2 (2010), 60-79.
  4. K. Chakraborty, S. Kanemitsu and X. -H. Wang, The modular relation and the digamma function, Kyushu Journal of Mathematics, Vol. 65,(2011), No. 1, 39-53.
  5. K. Chakraborty, S. Kanemitsu and H. Tsukada, Arithmetical Fourier series and the modular relation, Kyushu J. Math. Vol. 66, No. 2 (2012), 411-427.
  6. Kalyan Chakraborty, I. Katai and B.M. Phong, On Real Valued Additive Functions Modulo 1, Annales Univ. Sci. Budapest., Sect. Comp. No. 36 (2012), 355-373.
  7. Kalyan Chakraborty and Jay Mehta, A stamped Blind Signature Scheme based on Elliptic Curve Discrete Logarithm Problem, International Journal Of Network Security, Vol. 14, No. 6, 2012, 316-319.
  8. Kalyan Chakraborty and Jay Mehta, On Completely Multiplicative Complex Valued Functions, Annales Univ. Sci. Budapest, Sect. Comp. No. 38 (2012)
  9. K. Chakraborty, I. Katai and B. M. Phong, On additive functions satisfying some relations, Annales Univ. Sci. Budapest., Sect. Comp. 38 (2012) 1-12.
  10. K. Chakraborty, I. Katai and Bui Minh Phong, On the values of arithmetic functions in short intervals, Annales Univ. Sci. Budapest., Sect. Comp. 38 (2012) 13-21.
  11. Kalyan Chakraborty and Makoto minamide, On Partial Sums Of A Spectral Analogue Of The Mobius Function, Proc. Indian Acad. Sci. (Math. Sci.), Vol.123, No. 2, 2013, 193{201.
  12. K. Chakraborty, S. Kanemitsu and T. Kuzumaki, On The Class Number Formula of Certain Real Quadratic Fields, Hardy-Ramanujan Journal, 36, 1-7 (2013).
  13. Kalyan Chakraborty and Jay Mehta, Preventing unknown key-share attack using cryptographic bilinear maps, Journal of Discrete Mathematical Sciences and Cryptography, Vol. 17 (2014), No. 2, 135-147.
  14. K. Chakraborty, S. Kanemitsu and T. Kuzumaki, On the Barnes multiple gamma functions, Siauliai Mathematical Seminar, Vol. 9 (2014), No. 17, 27-41.
  15. Kalyan Chakraborty and Makoto Minamide, On Power moments Of The Hecke Multiplicative Functions, J. Aust. Math. Soc., Vol. 99 (2015), 334{340. 2015), doi: 10.1017/S1446788715000063.
  16. Kalyan Chakraborty, Shigeru Kanemitsu and Y. Sun, Codons and Codes, Pure and Applied Mathematics Journal, vol. 4 (2015), (2-1), 25-29.
  17. Tomihiro Arai, Kalyan Chakraborty and Jing Ma, Applications of the Hurwitz-Lerch zeta-function, Pure and applied Mathematics Journal, vol. 4 (2015), (2-1), 30-35.
  18. K. Chakraborty, S. Kanemitsu and H. Tsukada, Applications of the Beta-Transform, Siauliai Mathematical Seminar. Vol. 10 ( 2015), No. 18, 5-28.
  19. K. Chakraborty, S. Kanemitsu and H. -L. Li, Quadratic reciprocity and Riemann's non-di erentiable function, Research in Number Theory (2015) 1:14, DOI 10.1007/s40993-015-5.
  20. B. Maji, K. Chakraborty and S. Kanemitsu, Modular type relations associated to the Rankin-Selberg L-functions, Ramanujan J. August (2016), 1–15, doi:10.1007/s11139- 015-9759-8
  21. 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, 12 pp. 11B39 (11A25 11A67).
  22. Kalyan Chakraborty, Jorge Jimeńez Urroz and Francesco Pappalardi, Pairs of integers which are mutually squares, Sci China Math, 2017, 60, 1–14, doi: 10.1007/s11425- 016-0343-1.
  23. B. Maji, D. Banerjee, K. Chakraborty and S. Kanemitsu, Abel-Tauber process and asymptotic formulas (Accepted for publication in ’Kyushu Journal of Mathematics’).
  24. B. Maji, A. Juyal, K. Chakraborty and S.D. Kumar, Asymptotic expansion of a Lambert series (Accepted for publication in International Journal of Number Theory).

Other Publications

  1. K. Chakraborty, S. Kanemitsu, H. Kumagai and Y. Kubara, Shapes of objects and the golden ratio, Journal Of Sangluo University, Vol. 23 (2009), No. 4, 18-27.
  2. K. Chakraborty, S. Kanemitsu, Y. Katayama and Y. Nitta, Sustainibility of ancient constructions and non-associated numbers, Journal of Sangluo University, Vol. 24 (2010), No. 2, 60–79.
  3. Kalyan Chakraborty, Shigeru Kanemitsu and Y. Sun, Codons and Codes, Pure and Applied Mathematics Journal, Vol. 4 (2015), (2-1), 25–29.
  4. Kalyan Chakraborty, Y. Goto and Shigeru Kanemitsu, Music as mathematics of senses, (2015).

Conference Proceedings

  1. T. Arai, K. Chakraborty and S. Kanemitsu, On Modular Relations, Series on Number Theory and Its Applications, Vol. 11, (Plowing and Starring Through High Wave Forms: Edited By: M. Kaneko, S. Kanemitsu and Jianya Liu), Forthcoming (March 2015), Proceedings of the 7th China{Japan Seminar, World scienti c.
  2. Kalyan Chakraborty, On the divisibility of class numbers of real quadratic Fields, RIMS Conference Proceedings, Kyoto Univ., 2004.
  3. Kalyan Chakraborty, On the number of Fourier coecients that determine a form, Conference Proceedings, Institute of mathematics, Waseda University, 2005, 19-30.
  4. K. Chakraborty, H. Kanemitsu and H. -L. Li, Special functions in number theory and in science, Proceedings of the 14th Annual Conf. SSFA Vol. 14, (2015), 11–43.

Books

  • Kalyan Chakraborty, Shigeru Kanemitsu and Haruo Tsukada, Vistas of Special Functions II World Scientific, Singapore etc., 2009.
  • Kalyan Chakraborty, Shigeru Kanemitsu and T. Kuzumaki, A Quick Introduction to Complex Analysis, To be published by World Scienti c, Singapore.

Preprints

  1. K. Chakraborty, Some Problems in Number Theory, D. Phil Thesis, University of Allahabad, Allahabad.
  2. K. Chakraborty, Exponent of class groups of a family of cyclic cubic elds.
  3. K. Chakraborty, S. Kenmitsu and A. Laurinčikas, Complex powers of L-functions and integers without large prime factors
  4. Azizul Hoque and Kalyan Chakraborty, Divisibility of class number of certain families of quadratic fields
  5. Azizul Hoque and Kalyan chakraborty, Pell-type equations and class number of the maximal real subfield of a cyclotomic field.
  6. K. Chakraborty, A. Hoque, Y. Kishi and P.P. Pandey, Divisibility of the class numbers of imaginary quadratic fields.
  7. S. Banerjee, A. Hoque and K. Chakraborty, On the product of two Dedekind zeta functions.
  8. Kalyan Chakraborty, Azizul Hoque and Raj Kumar Mistri, Imaginary quadratic fields with class number not divisible by a given integer.

Current Projects

  1. GNFS: Aimed at Development of Modules and Tools for solving Integer factorisation and Discrete log Problems using Number Field Sieve, DRDO is funding this Project. Specially involved in developing the square root module.
  2. L-functions: Study the asymptotic behaviour of ‘Riesz sums’ associated to the Rankin-Selberg L-functions involving various automorphic foms ( e.g. harmonic Mass forms and Hasse-Weil zeta functions associated to the elliptic curves, Hilbert modular forms of degree 2. (With S. Banerjee and A. Juyal).
  3. 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 contract 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.

  4. 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 case 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. Its worth looking into these direction 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.