Bounds for a spectral exponential sum
Journal article, 2019

We prove new upper bounds for a spectral exponential sum by refining the process by which one evaluates mean values of L-functions multiplied by an oscillating function. In particular, we introduce a method which is capable of taking into consideration the oscillatory behaviour of the function. This gives an improvement of the result of Luo and Sarnak when T > X1/6+2 theta/3+epsilon. Furthermore, this proves the conjecture of Petridis and Risager in some ranges. Finally, this allows obtaining a new proof of the Soundararajan-Young error estimate in the prime geodesic theorem.


Olga Balkanova

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

Dmitry Frolenkov

Natl Res Univ

Russian Academy of Sciences

Journal of the London Mathematical Society

0024-6107 (ISSN) 1469-7750 (eISSN)

Vol. 99 2 249-272


Basic sciences

Subject Categories

Probability Theory and Statistics

Signal Processing

Mathematical Analysis



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7/2/2019 2