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Accessible Unlicensed Requires Authentication Published by De Gruyter June 5, 2017

Character sums with an explicit evaluation

Badria Alsulmi, Vincent Pigno and Christopher Pinner
From the journal Mathematica Slovaca

Abstract

We show that for Dirichlet characters χ, χ1, …, χs mod pm the sum

x1=1pmxs=1pmχ1(x1)χs(xs)χ(A1x1++Asxs+Bx1w1xsws)

has a simple evaluation when m is sufficently large, for m ≥ 2 if

p2A1AsB(1w1ws).

(Communicated by Federico Pellarin)


References

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Received: 2015-3-26
Accepted: 2015-8-6
Published Online: 2017-6-5
Published in Print: 2017-6-27

© 2017 Mathematical Institute Slovak Academy of Sciences