Research
May 6, 2023
1 min read
Updated: Jul 28
Publications:
1) " A Heron triangle and a Diophantine equation." Periodica Mathematica Hungarica 86 (2023), 530–537. https://doi.org/10.1007/s10998-022-00491-5. arXiv preprint (https://arxiv.org/abs/2105.03957)
(With Shamik Das and Debopam Chakraborty ).
2) "Construction of an infinite family of elliptic curves of 2-Selmer rank 1 from heron triangles." Research in Number Theory 8, 101 (2022). https://doi.org/10.1007/s40993-022-00411-z arXiv preprint (https://arxiv.org/abs/2206.02475) (with Debopam Chakraborty and Anupam Saikia).
One can find the codes to know the 2-Selmer rank and the rank of the elliptic curves via MAGMA and SAGE below.
3) " Size of the 2 Selmer groups for Heronian elliptic curves"
European journal of Mathematics 9 (2023), 107. https://doi.org/10.1007/s40879-023-00704-2(with Debopam Chakraborty).
arXiv preprint (https://arxiv.org/abs/2301.08099 )
Preprints:
1) "Class number divisibility of Q(√3p, √(m- 21pn²) ) constructed from elliptic curves of 2-Selmer rank exactly 1" (with Debopam Chakraborty and MD Imdadul Islam).
arXiv preprint (https://arxiv.org/abs/2212.11178 ).
Codes to know the class number of quadratic and biquadratic number fields using MAGMA
2) "A Diophantine Criterion for Shafarevich- Tate Groups of Elliptic Curves from Heron Triangles" arXiv preprint ( https://arxiv.org/abs/2301.03486).
3) "Elliptic curves associated with Heron triangles with high 2-Selmer rank" arXiv preprint (https://arxiv.org/abs/2308.00625) ( with Md Imdadul Islam and Debopam Chakraborty).
Please find my CV and a brief Research statement below, updated on 01/05/2023.
Funds
Project Name: Arithmetic Invariants of Heronian Elliptic Curves
Funding Agency: Centre for Interdisciplinary Studies and Research, D Y Patil International University, Pune
Grant No: CISR/2025SEPT/SM/007
Funding Amount: Rs. 10 L
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