Matrix Kloosterman sums modulo prime powers
M\'arton Erd\'elyi, \'Arp\'ad T\'oth, Gergely Z\'abr\'adi
TL;DR
This paper establishes optimal bounds for matrix Kloosterman sums modulo prime powers, extending previous results for prime moduli, with applications in the theory of horocyclic flow on GL_n.
Contribution
It provides the first optimal bounds for matrix Kloosterman sums modulo prime powers, broadening the scope of earlier prime modulus results.
Findings
Derived optimal bounds for matrix Kloosterman sums modulo prime powers.
Extended previous prime modulus results to prime power moduli.
Connected exponential sum bounds to the theory of horocyclic flow on GL_n.
Abstract
We give optimal bounds for matrix Kloosterman sums modulo prime powers extending earlier work of the first two authors on the case of prime moduli. These exponential sums arise in the theory of the horocyclic flow on .
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Taxonomy
TopicsAnalytic Number Theory Research · Algebraic Geometry and Number Theory · Advanced Algebra and Geometry