Character sums with an explicit evaluation

In: Mathematica Slovaca, vol. 67, no. 3

Badria Alsulmi - Vincent Pigno - Christopher Pinner

Details:

Year, pages: 2017, 623 - 630

Keywords:

character sums, Gauss sums

DOI: https://doi.org/10.1515/ms-2016-0296

About article:

We show that for Dirichlet characters $χ,χ₁,…,χ_s$ mod $p^m$ the sum

$$ ∑_x₁=1^{p^m} … ∑_{x_s=1}^{p^m}χ₁(x₁)… χ_s(x_s)χ(A₁x₁ + … + A_sx_s + Bx₁^w₁… x_s^w_s) $$

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

$$ p\nmid 2A₁… A_sB(1-w₁-… -w_s). $$

How to cite:

ISO 690:

Alsulmi, B., Pigno, V., Pinner, C. 2017. Character sums with an explicit evaluation. In Mathematica Slovaca, vol. 67, no.3, pp. 623-630. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0296

APA:

Alsulmi, B., Pigno, V., Pinner, C. (2017). Character sums with an explicit evaluation. Mathematica Slovaca, 67(3), 623-630. 0139-9918. DOI: https://doi.org/10.1515/ms-2016-0296

About edition:

Published: 27. 6. 2017