Large sets of consecutive Maass forms and fluctuations in the Weyl remainder

Holger Then

Research output: Working paperWorking paper and Preprints

Abstract

We explore an algorithm which systematically finds all discrete eigenvalues of an analytic eigenvalue problem. The algorithm is more simple and elementary as could be expected before. It consists of Hejhal's identity, linearisation, and Turing bounds. Using the algorithm, we compute more than one hundredsixty thousand consecutive eigenvalues of the Laplacian on the modular surface, and investigate the asymptotic and statistic properties of the fluctuations in the Weyl remainder. We summarize the findings in two conjectures. One is on the maximum size of the Weyl remainder, and the other is on the distribution of a suitably scaled version of the Weyl remainder.
Original languageEnglish
Publication statusPublished - 13 Dec 2012

Keywords

  • Mathematics - Number Theory
  • Mathematical Physics
  • 65N25
  • 11N45 (primary)
  • 11F41
  • 11Y16
  • 65-05 (secondary)

Fingerprint

Dive into the research topics of 'Large sets of consecutive Maass forms and fluctuations in the Weyl remainder'. Together they form a unique fingerprint.

Cite this