Algebra & Number Theory

Some sums over irreducible polynomials

David Speyer

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1513090726

Digital Object Identifier
doi:10.2140/ant.2017.11.1231

Mathematical Reviews number (MathSciNet)
MR3671435

Zentralblatt MATH identifier
06748170

Subjects
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

Keywords
zeta function special value function field

Citation

Speyer, David. Some sums over irreducible polynomials. Algebra Number Theory 11 (2017), no. 5, 1231--1241. doi:10.2140/ant.2017.11.1231. https://projecteuclid.org/euclid.ant/1513090726


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References

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  • T. Tao, “Polymath proposal: explaining identities for irreducible polynomials”, 2015, https://polymathprojects.org/2015/12/28/.
  • D. S. Thakur, “Surprising symmetries in distribution of prime polynomials”, preprint, 2015.