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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 and , we count positive integers with 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 be a genus two cuspidal Siegel modular eigenform. We prove an adelic open image theorem for the compatible system of Galois representations associated to , generalising…