Probabilistic and Analytic Number Theory.
-
Distribution of moments of Hurwitz class numbers in arithmetic progressions and holomorphic projection (with B. Kane), (to appear in Trans. Amer. Math. Soc.), Arxiv link: arXiv:2010.15325.
-
Formulas for moments of class numbers in arithmetic progressions, (with K. Bringmann and B. Kane), (to appear in Acta Arithmetica), Arxiv link: arXiv:2109.07325.
-
Sato-Tate distribution of p-adic hypergeometric functions, (with N. Saikia), (to appear in Research in Number Theory), Arxiv link: arXiv:2207.10375.
-
On signatures of elliptic curves and modular forms, (with A. Dąbrowski and J. Pomykała), (to appear in Ramanujan J).
-
Turán inequalities for the plane partition function, (with K. Ono and L. Rolen), (to appear in Advances of Mathematics), Arxiv link: arXiv:2201.01352.
-
A Bombieri-Vinogradov-type theorem with prime power moduli, (with S. Baier), Acta Arithmetica 204 (2022), 115-140.
-
On the normal number of prime factors of sums of Fourier coefficients of eigenforms, (with M. R. Murty and V. K. Murty), J. Number Theory, 233 (2022), 59-77.
-
Distribution of signs of Karatsuba's and generalized Davenport-Heilbronn $Z$-functions, with M. K. Das, J. Number Theory, 212 (2020), 409-447.
-
Traces of Hecke operators in level 1 and p-adic hypergeometric functions, with N. Saikia, Ramanujan J 52, 519–539 (2020). doi:10.1007/s11139-019-00170-z.
-
Some remarks on the coefficients of symmetric power L-functions, with B. Kumar and J. Meher, Automorphic Forms and Related Topics, Contemporary Mathematics, Vol. 732, American Mathematical Society, (2019), 155-164.
-
Distinguishing pure representations by normalized traces, with M.K Pandey and J.P Saha, J. Number Theory, 195 (2019), 217--225.
-
Zeros of L-functions attached to cusp forms of half-integral weight, with J. Meher and K.D Shankhadhar, Proc. Amer. Math. Soc., 147 (2019), 131-143.
-
Zeros of $L$-functions attached to modular forms of half-integral weights, with J. Meher and K. Srinivas, Bull. Lond. Math. Soc., 49 (2017), 926-936.
-
Distinguishing Hecke eigenforms, with M. R. Murty, Proc. Amer. Math. Soc., 145 (2017), 1899-1904.
-
Sign changes of coefficients of certain Dirichlet series, with J. Meher and K. D. Shankhadhar, Funct. Approx. Comment. Math., 52 (2015), Part 1, 117–126.
-
A Bombieri-Vinogradov-type theorem for moduli with small radical, (with S. Baier), Arxiv link: arXiv:2212.0557.
-
Odd moments for the trace of Frobenius and the Sato--Tate conjecture in arithmetic progressions, (with K. Bringmann and B. Kane), (submitted), Arxiv link: arXiv:2112.08205. All R
-
An all-purpose Erdos-Kac theorem, (with M. R. Murty and V. K. Murty), 2021, 15 pages, (submitted), (available on request).
-
Zeros of higher derivatives of Riemann zeta function, (with M. K. Das), 2020, 40 pages, (preprint) (pdf).
-
Effective joint equidistribution of eigenvalues of Hecke operators, (Arxiv link: arXiv:1703.07944).
-
Distribution of gaps of eigenangles of Hecke operators, (submitted), (Arxiv link: http://arxiv.org/pdf/1603.06249.pdf).
-
Even Semester, 2023: I am teaching M561 (Elliptic Curves).
-
Odd Semester, 2022: MA601 - Algebra I (Graduate course).
-
Spring semester, 2022: M308 (Complex Analysis).
Invited talks:
-
2022 (May 17th) International Seminar On Automorphic forms (ETH Zurich and TU Darmstadt), Sato-Tate conjecture in arithmetic progressions for certain families of elliptic curves.
-
2022 (25th-26th March) In-House Symposium 2022, IISER Bhopal, A Bombieri-Vinogradov-type theorem with prime power moduli.
-
2022 (January 11th) Intercollegiate Cryptology Seminar, Warsaw, Poland, On the normal number of prime factors of sums of Fourier coefficients of eigenforms.
-
2021 (December 29th) Webinar on Number Theory, Utkal University, Probabilistic methods in modular forms.
-
2021 (October 5th) Number theory seminar, Charles University, Arithmetic and statistics of sums of eigenvalues of Hecke operators.
-
2021 (August 27th) Ramakrishnan mission Vivekananda Educational and Research Institute, Distribution of moments of trace of Frobenius in arithmetic progressions and holomorphic projection.
-
2021 (August 20th) International webinar on Introduction and applications of Cryptography and Graph theory, B.J.B College, Mathematics in dailey life.
-
2021 (March 24th) Texas Tech University, Algebra and Number theory seminar, Arithmetic and statistics of sums of eigenvalues of Hecke operators.
-
2021 (March 8th) Institute of Mathematics Polish Academy of Science, Warsaw Number theory seminar, Arithmetic and statistics of sums of eigenvalues of Hecke operators.
-
2019 (11th March) The University of Ohio, Ohio State Number Theory Student Seminar, Distribution of signs and zeros of generalised Davenport-Heilbronn function.
-
2019 (5th March) Duquesne University, Pittsburgh, Graduate Student Workshop, Probabilistic methods and modular forms.
-
2018 (16th July-21th July) The University of Hong Kong, 2018 HKU Number Theory Days, Zeros of Dirichlet series attached to half-integral weight cusp forms.
-
2018 (4th January) Indian Institute of Technology, Guwahati, IITG Mathematics Seminar series, In the neighborhood of Sato-Tate conjecture.
-
2017 (21st March) Jawaharlal Nehru University, In the neighborhood of Sato-Tate conjecture.
-
2017 (14th March) The University of Illinois at Urbana-Champaign, Number Theory Seminar, In the neighborhood of Sato-Tate conjecture.
-
2017 (14th March) The University of Illinois at Urbana-Champaign, U.S.A, Spring 2017, UIUC: MATH 532 Analytic Theory of Numbers II, Effective joint distribution of eigenvalues of Hecke operators.
-
2016 (21th December - 27th December) National Institute of Science Education and Research, Discussion meeting on Automorphic forms, Arithmetic statistics of Automorphic forms.
-
2016 (7th September) Harichchandra Research Institute, Allahabad, 70-th Birthday conference of prof. M. Waldschmidt, Statistics of eigenvalues of Hecke operators.
-
2016 (4th September) IISER Bhopal, Conference on Modular Forms, Arithmetic statistics of modular forms.
-
2016 (13th June - 2nd July): Teaching assistant, Advanced Instructional School on Analytic theory of algebraic numbers, Bhubaneswar, (Basic Algebraic number theory).
-
2015 Advanced Instructional School on Analytic number theory, Bhubaneshwar (Teaching Assistant), Equidistribution theory, Beurling- Selberg polynomials and Eichler - Selberg trace formula.
Contributed talks:
-
2022 (20th - 24th June) Equidistribution and Arithmetic Dynamics, Oklahoma State University, Sato-Tate conjecture in arithmetic progressions for certain families of elliptic curves.
-
2021 (2nd October - 3rd October) 2021 Maine-Quebec Number Theory Conference, Distribution of moments of traces of Frobenious in arithmetic progression.
-
2021 (25th September - 26th September) PAlmetto Joint Arithmetic, Modularity, and Analysis Series (PAJAMAS)-III, An all purpose Erdos-Kac theorem.
-
2020 (26th September-27th September) Université Laval, 2020 Quebec-Maine Number Theory Conference, On the normal number of prime divisors of sum of eigenvalues of Hecke operators.
-
2020 (19th September-20th September) PAlmetto Joint Arithmetic, Modularity, and Analysis Series, Arithmetic and statistics of sums of eigenvalues of Hecke operators.
-
2019 (6th March-10th March) Duquesne University, 33rd Automorphic Forms Workshop, Zeros of Dirichlet series attached to half-integral weight cusp forms and generalised Davenport-Heilbronn function.
-
2017 (6th March-9th March) East Tennessee State University, U.S.A, 31st Automorphic Forms Workshop, Distinguishing Hecke eigenforms.
-
2016 (7th March-10th March) Wake Forest University, U.S.A, 30-th Automorphic Forms Workshop, Distribution of gaps of eigenangles of Hecke operators.
Popular talks:
-
2020 (28th August) Arya Vidyapeeth College, Mathematics in daily life.
-
2018 (22th February) Harish-Chandra Research Institute, National Science Day 2018, Fun in Mathematics (Popular talk) (pdf).