Year: 2017
Type: article
Abstract: In this article, we prove an Omega result for the Hecke eigenvalues λ F ( n ) {\lambda_{F}(n)} of Maass forms F which are Hecke eigenforms in the space of Siegel modular forms of weight k, genus two for the Siegel modular group S p 2 ( ℤ ) {Sp_{2}({\mathbb{Z}})} . In particular, we prove λ F ( n ) = Ω ( n k - 1 exp ( c log n log log n ) ) , \lambda_{F}(n)=\Omega\biggl{(}n^{k-1}\exp\biggl{(}c\frac{\sqrt{\log n}}{\log% \log n}\biggr{)}\biggr{)}, when c > 0 {c>0} is an absolute constant. This improves the earlier result λ F ( n ) = Ω ( n k - 1 ( log n
Source: Forum Mathematicum
Authors: Sanoli Gun, Biplab Paul, Jyoti Sengupta
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2963829344