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Mathematics > Number Theory

arXiv:1411.7600 (math)
[Submitted on 27 Nov 2014]

Title:Selberg sums - a new perspective

Authors:Samuel J. Patterson
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Abstract:Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in in 1940s. The original versions of these sums were introduced by this http URL in 1981 and, following an elegant idea of this http URL in 1991 they were evaluated by Anderson, Evans and P.B.~van~Wamelen. In 2007 the author noted that these sums and certain generalizations of them appear in the study of the distribution of Gauss sums over a rational function field over a finite field. The distribution of Gauss sums is closely related to the distribution of the values of the discriminant of polynomials of a fixed degree. Here we shall take this up further. The main goal here is to establish the basic properties of Selberg sums and to formulate the problems which arise from this point of view.
Comments: 14 pages
Subjects: Number Theory (math.NT)
MSC classes: 11T24
Cite as: arXiv:1411.7600 [math.NT]
  (or arXiv:1411.7600v1 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.1411.7600

Submission history

From: Samuel Patterson [view email]
[v1] Thu, 27 Nov 2014 13:47:18 UTC (11 KB)
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