Published Papers
Published Papers
Embedded Files
Elliptic surfaces to class groups and Selmer groups (Kalyan Banerjee and Kalyan Chakraborty), Research in Number Theory, (to appear). arXiv: 2509.00551
On the exponential Diophantine equation $cx^2+p_1^{2m_1}p_2^{2m_2}\cdots p_r^{2m_r}=4y^q$ (with Kotyada Srinivas and Usha K. Sangale), Journal of Ramanujan Mathematical Society, (to appear).
On the plus parts of the class numbers of cyclotomic fields (with Kalyan Chakraborty), Chinese Annals of Mathematics, Series B, 46 (2025), no. 2, 1--10. arXiv: 2310.07501
Chow groups, pull back and class groups (with Kalyan Banerjee), Monatshefte für Mathematik, 205 (2024), no. 3, 433--454. arXiv: 1903.04210
On a class of Lebesgue-Ramanujan-Nagell equations, Periodica Mathematica Hungarica, 88 (2024), no. 2, 418--428. arXiv: 2005.05214
Diophantine $D(n)$-quadruples in $\mathbb{Z}[\sqrt{4k+2}]$ (with Kalyan Chakraborty and Shubham Gupta), Glasnik Matematicki 59 (2024), no. 2, 259-276. arXiv: 2302.04145
Parameterized Families of Quadratic Fields with n-Rank at Least 2 (with Katyada Srinivas), Class Groups of Number Fields and Related Topics, 125–131, Springer Proc. Math. Stat., 470, Springer, Singapore, 2024. arXiv: 2412.20080
A remark on a Diophantine equation of S. S. Pillai, Czechoslovak Mathematical Journal, 74 (2024), no. 3, 897--903.
On the exponential Diophantine equation $x^2+p^mq^n=2y^p$ (with Kalyan Chakraborty), New Zealand Journal of Mathematics 55 (2024), 53--60. arXiv:2308.12708
Complete solutions of a Lebesgue-Ramanujan-Nagell type equation (with Priyanka Baruah and Anup Das), Archivum Mathematicum, 60 (2024), 135--145. arXiv:2104.12680
Lehmer sequence approach to the divisibility of class numbers of imaginary quadratic fields (with Kalyan Chakraborty), The Ramanujan Journal, 60 (2023), no. 4, 913--923. arXiv:2210.00561
Diophantine triples with the property $D(n)$ for distinct $n$'s (with Kalyan Chakraborty and Shubham Gupta), Mediterranean Journal of Mathematics, 20 (2023), no. 1, 13pp, article no. 31. arXiv: 2204.14208
On a conjecture of Franu\vsi\'c and Jadrijevi\'c: Counter-examples (with Kalyan Chakraborty and Shubham Gupta), Results in Mathematics, 78 (2023), no. 1, 14pp, article no. 18. arXiv: 2211.05010
On a conjecture of Iizuka, Journal of Number Theory, 238 (2022), 464--473. arXiv: 2106.00395
On the Diophantine equation $dx^2+p^{2a}q^{2b}=4y^p$ (with Kalyan Chakraborty), Results in Mathematics, 77 (2022), no. 1, 11pp, article no. 18. arXiv: 2106.01964
Generalized Mersenne numbers of the form $cx^2$, Annales Mathematicae et Informaticae, 55 (2022), 88--92. arXiv: 2205.06235
On the exponents of class groups of some families of imaginary quadratic fields, Mediterranean Journal of Mathematics, 18 (2021), no. 4, 13pp. article no. 153. arXiv: 2005.12512
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
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
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. arXiv: 2011.01099
Class number one problem for the real quadratic fields $\mathbb{Q}(\sqrt{n^2+2r})$ (with Srinivas Kotyada), Archiv der Mathematik, 116 (2021), no. 1, 33--36. arXiv: 2008.03505
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
Exponents of class groups of certain imaginary quadratic fields (with Kalyan Chakraborty), Czechoslovak Mathematical Journal, 70 (2020), no. 4, 1167--1178. arXiv:1801.00392
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
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. arXiv: 1812.02488v3
Complete solution to Cyclotomy of order $2\ell^2$ with prime $\ell$ (with Md. Helal Ahmed, Jagmohan Tanti), The Ramanujan Journal, 53 (2020), no. 3, 529--550. arXiv: 1807.07708
Divisibility of Selmer groups and class groups (with Kalyan Banerjee, Kalyan Chakraborty), Hardy-Ramanujan Journal, 42 (2019), 85--99. arXiv: 1912.02420
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. arXiv: 1712.07338
On the solutions of a Lebesgue - Nagell type equation (with Shanjay Batter, Richa Sharma), Acta Mathematica Hungarica, 158 (2019), no. 1, 17--26. arXiv.1810.04512
Pell-type equations and class number of the maximal real subfield of a cyclotomic field (with Kalyan Chakraborty), The Ramanujan Journal, 46 (2018), no. 3, 727--742. arXiv: 1710.09760
Divisibility of the class numbers of imaginary quadratic fields (with Kalyan Chakraborty, Yasuhiro Kishi, Prem Prakash Pandey), Journal of Number Theory, 185 (2018), 339--348. arXiv: 1710.03662
Class groups of imaginary quadratic fields of 3-rank at least 2 (with Kalyan Chakraborty), Ann. Univ. Sci. Budapest. Sect. Comput.47 (2018), 179--183. (in a special issue in honor of the 80-th birthday of Professors Zoltán Daróczy and Imre Kátai, the 75-th birthday of Professor Karl-Heinz Indlekofer, the 70-th birthday of Professors Jean-Marie De Koninck and Gyula Maksa, the 65-th birthday of Professor Bui Minh Phong and the 60-th birthday of Professor Sándor Fridli). arXiv:1802.07919v1
On $\xi$-torsion modules (with Himashree Kalita, Helen K. Saikia), Bollettino dell'Unione Matematica Italiana, 10 (2017), no. 2, 223--228. PDF
On the class-number of the maximal real subfield of a cyclotomic field (with Helen K. Saikia), Quaestiones Mathematicae, 37 (2016), no. 7, 889--894. PDF
On the divisibility of class numbers of quadratic fields and the solvability of Diophantine equations (with Helen K. Saikia), SeMA Journal, 73 (2016), no. 3, 213--217. arXiv: 1710.09755
A new cryptosystem using generalized Mersenne primes, SeMa Journal, 73 (2016), 77--83.
Some aspects of quasi-pseudo principally injective modules (with Hemen Dutta, Sameer M. Saeed), Journal of the Ramanujan Mathematical Society, 31 (2016), no. 3, 257--263. arXiv: 1909.10311
A note on quadratic fields whose class numbers are divisible by 3 (with Helen K. Saikia), SeMA Journal, 73 (2016), no. 1, 1--5.
On the exponential Diophantine equation $(M_{pq}+1)^x+M_{pq}^y=z^2$, European Journal of Pure and Applied Mathematics, 09 (2016), no. 2, 240--243.
On generalized Mersenne primes and class numbers of equivalent quadratic fields and cyclotomic fields (with Helen K. Saikia), SeMA Journal, 67 (2015), no. 1, 71--75.
A family of imaginary quadratic fields whose class numbers are multiples of three (with Helen K. Saikia), Journal of Taibah University for Sciences, 9 (2015), no. 3, 399--402.
On generalized Mersenne prime (with Helen K. Saikia), SeMA Journal, 66 (2014), no. 1, 1--7.
Book/Edited Volume
Book/Edited Volume
Class Groups of Number Fields and Related Topics (with Kalyan Chakraborty, Prem Prakash Pandey), Springer Proc. Math. Stat. 470, 246+XII pages, Springer, Singapore, 2024 (edited).
Class groups of number fields and related topics (ICCGNFRT-2017 and 2018) (with Kalyan Chakraborty, Prem Prakash Pandey), 178+XII pages, Springer Singapore, 2020 (edited).
Expository Papers/Proceedings/Book Chapters
Expository Papers/Proceedings/Book Chapters
Divisibility of class numbers of quadratic fields: Qualitative aspects (with Kalyan Chakraborty, Richa Sharma). In: Agarwal P., Dragomir, S. S., Jleli, M., Samet, B . (eds) Advances in Mathematical inequalities and Application. Trends in Mathematics. Birkhäuser,/Springer, Singapore, 2018, pp. 247--264. PDF
Quadratic Reciprocity and Some“Non-differentiable” Functions (with Kalyan Chakraborty), In: Ruzhansky M., Cho Y., Agarwal P., Area I. (eds) Advances in Real and Complex Analysis with Applications. Trends in Mathematics. Birkhäuser/Springer, Singapore, 2017, pp. 145--181. PDF
Generalized perfect numbers connected with arithmetic functions (with Himashree Kalita), Mathematical Sciences Letters, 03 (2014), no. 03, 249--253.
Preprints
Preprints
Branched covers of $\mathbb{P}^1$ and divisibility of class group (Kalyan Banerjee and Kalyan Chakraborty), submitted.
On the Diophantine equation $dx^2+p^{2m}=2y^n$ (with Alain Togbe), Preprint PDF
On the Lebesgue-Ramanujan-Nagell type equation $x^2+17^k41^\ell59^m=2^\delta y^n$ (with Kalyan Chakraborty), submitted.
Fields with small class group in the family $\mathbb{Q}(\sqrt{9m^2+2m})$ (with Kalyan Chakraborty), submitted.
On the simultaneous 3-divisibility of class numbers of quadruples of real quadratic fields (with Kalyan Banerjee and Ankurjyoti Chutia), submitted.
On the purely exponential Diophantine equation $(11pm^2 - 1)^x+(p(p - 11)m^2 + 1)^y=(pm)^z$ (with Arunabh Gogoi and Jyotishman Kalita), submitted.
Class number divisibility of tuples of imaginary quadratic fields: `a la Iizuka, submitted.
A note on a conjecture of Terai and Shinsho (with Arunabh Gogoi and Jyotishman Kalita), submitted.
A note on rank zero quadratic twists of a Mordell curve (with Ankurjyoti Chutia and Jyotishman Kalita), submitted.
Some results on the exponents of class groups of imaginary quadratic fields (with Ankurjyoti Chutia), submitted.
Page updated
Google Sites
Report abuse