Sums of Kloosterman sums in the prime geodesic theorem

2018/03/12 by Balkanova, Olga, Frolenkov, Dmitry · 1 citation
#FOS: Mathematics #Number Theory (math.NT) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.1803.04206

Abstract

We develop a new method for studying sums of Kloosterman sums related to the spectral exponential sum. As a corollary, we obtain a new proof of the estimate of Soundararajan and Young for the error term in the prime geodesic theorem.

Cited by

• The hyperbolic lattice counting problem in large dimensions

Related

• Matrix Kloosterman sums modulo prime powers
• The Prime Geodesic Theorem and Bounds for Character Sums
• On the support of the Kloosterman paths
• Distribution of prime geodesic traces
• Sums of Kloosterman sums over primes in an arithmetic progression