Numerical computations with the trace formula and the Selberg eigenvalue conjecture

Andrew R. Booker, Andreas Strömbergsson

Type: Article

Publication Date: 2007-01-27

Citations: 28

DOI: https://doi.org/10.1515/crelle.2007.047

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.

Locations

CiteSeer X (The Pennsylvania State University) - View - PDF
Journal für die reine und angewandte Mathematik (Crelles Journal) - View

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