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On the value distribution and moments of the Epstein zeta function to the right of the critical strip
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics.
2011 (English)In: Journal of Number Theory, ISSN 0022-314X, E-ISSN 1096-1658, Vol. 131, no 7, 1176-1208 p.Article in journal (Refereed) Published
Abstract [en]

We study the Epstein zeta function E-n(L, S) for s > n/2 and a random lattice L of large dimension n. For any fixed c > 1/2 we determine the value distribution and moments of E-n(., cn) (suitably normalized) as n -> infinity. We further discuss the random function C -> E-n(., cn) for c is an element of [A, B] with 1/2 < A < B and determine its limit distribution as n -> infinity.

Place, publisher, year, edition, pages
2011. Vol. 131, no 7, 1176-1208 p.
Keyword [en]
Lattices, Epstein's zeta function, Value distribution, Moments
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Research subject
URN: urn:nbn:se:uu:diva-132642DOI: 10.1016/j.jnt.2010.12.003ISI: 000289178500002OAI: oai:DiVA.org:uu-132642DiVA: diva2:358671
Available from: 2010-10-23 Created: 2010-10-23 Last updated: 2012-02-16Bibliographically approved

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Analysis and Applied Mathematics
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