Numerical computations with the trace formula and the Selberg eigenvalue conjecture

AR Booker, A Strömbergsson

Research output: Contribution to journalArticle (Academic Journal)peer-review

16 Citations (Scopus)

Abstract

We verify the Selberg eigenvalue conjecture for congruence groups of small squarefree conductor, improving on a result of Huxley [M. N. Huxley, Introduction to Kloostermania, in: Elementary and analytic theory of numbers, Banach Center Publ. 17, Warsaw (1985), 217-306.]. The main tool is the Selberg trace formula which, unlike previous geometric methods, allows for treatment of cases where the eigenvalue 1/4 is present. We present a few other sample applications, including the classification of even 2-dimensional Galois representations of small squarefree conductor.
Translated title of the contributionNumerical computations with the trace formula and the Selberg eigenvalue conjecture
Original languageEnglish
Pages (from-to)113 - 161
Number of pages49
JournalJournal für die reine und angewandte Mathematik
Volume2007 (607)
DOIs
Publication statusPublished - Jun 2007

Bibliographical note

Publisher: de Gruyter

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