Singular Gauss sums, Polya–Vinogradov inequality for GL(2) and growth of primitive elements
Article Type
Research Article
Publication Title
Mathematische Annalen
Abstract
We establish an analogue of the classical Polya–Vinogradov inequality for GL(2 , Fp) , where p is a prime. In the process, we compute the ‘singular’ Gauss sums for GL(2 , Fp). As an application, we show that the collection of elements in GL(2 , Z) whose reduction modulo p are of maximal order in GL(2 , Fp) and whose matrix entries are bounded by x has the expected size as soon as x≫ p1/2+ε for any ε> 0.
First Page
943
Last Page
985
DOI
https://10.1007/s00208-022-02413-9
Publication Date
6-1-2023
Recommended Citation
Ganguly, Satadal and Rajan, C. S., "Singular Gauss sums, Polya–Vinogradov inequality for GL(2) and growth of primitive elements" (2023). Journal Articles. 3725.
https://digitalcommons.isical.ac.in/journal-articles/3725
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