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2017 Some sums over irreducible polynomials
David Speyer
Algebra Number Theory 11(5): 1231-1241 (2017). DOI: 10.2140/ant.2017.11.1231

Abstract

We prove a number of conjectures due to Dinesh Thakur concerning sums of the form Ph(P) where the sum is over monic irreducible polynomials P in Fq[T], the function h is a rational function and the sum is considered in the T1-adic topology. As an example of our results, in F2[T], the sum P1(Pk 1) always converges to a rational function, and is 0 for k = 1.

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David Speyer. "Some sums over irreducible polynomials." Algebra Number Theory 11 (5) 1231 - 1241, 2017. https://doi.org/10.2140/ant.2017.11.1231

Information

Received: 17 October 2016; Accepted: 3 April 2017; Published: 2017
First available in Project Euclid: 12 December 2017

zbMATH: 06748170
MathSciNet: MR3671435
Digital Object Identifier: 10.2140/ant.2017.11.1231

Subjects:
Primary: 11M38
Secondary: 05E05 , 11M32

Keywords: function field , special value , zeta function

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.11 • No. 5 • 2017
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