A lower bound for classical Kloosterman sums and an application
Abstract
In this paper, we present a lower bound for the classical Kloosterman sum [Formula: see text] where [Formula: see text] and c is an odd integer. We apply this lower bound for Kloosterman sums to derive an explicit lower bound in Petersson’s trace formula, subject to a given condition. Consequently, we achieve a modified version of Theorem 1.7 from J. Jung and N. Talebizadeh Sardari [Asymptotic trace formula for the Hecke operators, Math. Ann. 378(1–2) (2020) 513–557], where weight k and level N are permitted to vary independently. Using this modified version, we get a lower bound for a weighted trace of the Hecke operator [Formula: see text] acting on the space [Formula: see text], of cusp forms of weight k and level N with [Formula: see text].
Fields of Study & Subjects
Analytic Number Theory Research
Limits and Structures in Graph Theory
Publication details
- Journal / source
- International Journal of Number Theory
- Publisher
- World Scientific Pub Co Pte Ltd
- Volume
- 22
- Issue
- 05
- Pages
- 1125–1140
- Publication date
- 16 January 2026
- Language
- EN