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Numerical computations with the trace formula and the Selberg eigenvalue conjecture
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2007 (English)In: Journal für die Reine und Angewandte Mathematik, ISSN 0075-4102, E-ISSN 1435-5345, Vol. 2007, no 607, 113-161 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2007. Vol. 2007, no 607, 113-161 p.
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Mathematics
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URN: urn:nbn:se:uu:diva-12616DOI: 10.1515/CRELLE.2007.047ISI: 000248576400004OAI: oai:DiVA.org:uu-12616DiVA: diva2:40385
Available from: 2008-01-08 Created: 2008-01-08 Last updated: 2017-12-11Bibliographically approved

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Strömbergsson, Andreas

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