Algebra & Number Theory
- Algebra Number Theory
- Volume 11, Number 5 (2017), 1231-1241.
Some sums over irreducible polynomials
We prove a number of conjectures due to Dinesh Thakur concerning sums of the form where the sum is over monic irreducible polynomials in , the function is a rational function and the sum is considered in the -adic topology. As an example of our results, in , the sum always converges to a rational function, and is for .
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
Permanent link to this document
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
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