Algebra & Number Theory

Some sums over irreducible polynomials

David Speyer

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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.

Article information

Algebra Number Theory, Volume 11, Number 5 (2017), 1231-1241.

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

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11M38: Zeta and $L$-functions in characteristic $p$
Secondary: 05E05: Symmetric functions and generalizations 11M32: Multiple Dirichlet series and zeta functions and multizeta values

zeta function special value function field


Speyer, David. Some sums over irreducible polynomials. Algebra Number Theory 11 (2017), no. 5, 1231--1241. doi:10.2140/ant.2017.11.1231.

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