Bounds for a spectral exponential sum
Artikel i vetenskaplig tidskrift, 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.

Författare

Olga Balkanova

Chalmers, Matematiska vetenskaper, Algebra och geometri

Göteborgs universitet

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

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

Signalbehandling

Matematisk analys

DOI

10.1112/jlms.12174

Mer information

Senast uppdaterat

2019-07-02