Selberg Sums: A New Perspective

Samuel J. Patterson ()
Additional contact information
Samuel J. Patterson: Mathematisches Institut

A chapter in From Arithmetic to Zeta-Functions, 2016, pp 353-365 from Springer

Abstract: Abstract Selberg sums are the analogues over finite fields of certain integrals studied by Selberg in 1940s. The original versions of these sums were introduced by R.J. Evans in 1981, and following an elegant idea of G.W. Anderson 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.

Keywords: Anderson–Evans–v.Wamelen theorem; Eisenstein series; Metaplectic groups; Rational function fields; Selberg sums; Primary 11T24; Secondary 11T55, 11F99 (search for similar items in EconPapers)
Date: 2016
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-28203-9_21

Ordering information: This item can be ordered from
http://www.springer.com/9783319282039

DOI: 10.1007/978-3-319-28203-9_21

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().