On the representation of integers as the sum of kht powers in the arithmetic progression

Authors:

Olga SAVASTRU, Pavel VARBANETS

AMS Classification:

11N37

Keywords:

asymptotic estimate, meromorphic continuation, Waring zeta-function

Abstract:

We investigate the behaviour of integers represented as the sum of kth powers in arithmetic progressions. Using the Waring zeta-function introduced by A. Vinogradov, we prove the asymptotic formula for the summatory function of the number of representations of m as the sum of kth powers in arithmetic progressions.

Download paper:

savastru-varbanets-08.pdf

Vol. 3 (11), 2008