Arvind Kumar

activity

20162023

most citedRegularity of powers of quadratic sequences with applications to binomial ideals

22 citations · 77 across the 21 of their papers we have counts for

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8 papers · 1 filter

math.NT2022

Coprimality of Fourier coefficients of eigenforms

Satadal Ganguly, Arvind Kumar, Moni Kumari

Given a pair of distinct non-CM normalized eigenforms having integer Fourier coefficients $a_{1} (n)$ and $a_{2} (n)$ , we count positive integers $n$ with $(a_{1} (n), a_{2} (n)) = 1$ and make…

math.NT2022

On signs of Hecke eigenvalues of Siegel eigenforms

Arvind Kumar, Jaban Meher, Karam Deo Shankhadhar

In this article, we distinguish Siegel cuspidal eigenforms of degree two on the full symplectic group from the signs of their Hecke eigenvalues. To establish our theorem, we obtain…

math.NT2022★ 1 cited

On the Lang--Trotter conjecture for Siegel modular forms

Arvind Kumar, Moni Kumari, Ariel Weiss

Let $f$ be a genus two cuspidal Siegel modular eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated to $f$ , generalising…

math.NT2021

Ramanujan-style congruences for prime level

Arvind Kumar, Moni Kumari, Pieter Moree +1

We establish Ramanujan-style congruences modulo certain primes $ℓ$ between an Eisenstein series of weight $k$ , prime level $p$ and a cuspidal newform in the $ε$ -eigens…

math.NT2021

Divisors of Fourier coefficients of two newforms

Arvind Kumar, Moni Kumari

For a pair of distinct non-CM newforms of weights at least 2, having rational integral Fourier coefficients $a_{1} (n)$ and $a_{2} (n)$ , under GRH, we obtain an estimate for the set…

math.NT2019

Reductions of Galois representations and the theta operator

Eknath Ghate, Arvind Kumar

Let $p \geq 5$ be a prime, and let $f$ be a cuspidal eigenform of weight at least $2$ and level coprime to $p$ of finite slope $α$ . Let $ρ ˉ_{f}$ denote the mod $p$ Galois representa…