Functiones et Approximatio Commentarii Mathematici

Jacobi-type sums with an explicit evaluation modulo prime powers

Badria Alsulmi, Vincent Pigno, and Christopher Pinner

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We show that for Dirichlet characters $\chi_1,\ldots ,\chi_s$ mod $p^m$ the sum $$ \mathop{\sum_{x_1=1}^{p^m} \dots \sum_{x_s=1}^{p^m}}_{ A_1x_1^{k_1}+\dots+ A_sx_s^{k_s}\equiv B \text{ mod } p^m}\chi_1(x_1)\cdots \chi_s(x_s), $$ has a simple evaluation when $m$ is sufficiently large.

Article information

Funct. Approx. Comment. Math., Volume 56, Number 1 (2017), 49-60.

First available in Project Euclid: 27 January 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11L10: Jacobsthal and Brewer sums; other complete character sums 11L40: Estimates on character sums
Secondary: 11L03: Trigonometric and exponential sums, general 11L05: Gauss and Kloosterman sums; generalizations

character sums Gauss sums Jacobi sums


Alsulmi, Badria; Pigno, Vincent; Pinner, Christopher. Jacobi-type sums with an explicit evaluation modulo prime powers. Funct. Approx. Comment. Math. 56 (2017), no. 1, 49--60. doi:10.7169/facm/1590.

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