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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


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


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


(Communicated by Federico Pellarin)


[1] Alsulmi, B.—Pigno, V.— Pinner, C.: Jacobi-type sums with an explicit evaluation modulo prime powers, (preprint at ), (to appear Funct. Approx. Comment. Math. (2017)).Search in Google Scholar

[2] Cochrane, T.: Exponential sums modulo prime powers, Acta Arith. 101 (2002), 131–149.Search in Google Scholar

[3] Cochrane, T.—Zheng, Z.: Pure and mixed exponential sums, Acta Arith. 91 (1999), 249–278.Search in Google Scholar

[4] Cochrane, T.—Zheng, Z.: A survey on pure and mixed exponential sums modulo prime powers. In: Number theory for the millennium I, Urbana, IL, 2000, pp. 273–300.Search in Google Scholar

[5] Long, M.—Pigno, V.—Pinner, C.: Evaluating prime power Gauss and Jacobi sums, arXiv:1410.6179 [math.NT], (to appear Tamkang J. Math.)Search in Google Scholar

[6] Pigno, V.—Pinner, C.: Binomial character sums modulo prime powers, J. Théor. Nombres Bordeaux 28 (2016), 39–53.Search in Google Scholar

[7] Pigno, V.—Pinner, C.—Sheppard, J.: Evaluating binomial character sums modulo powers of two, J. Math. Res. Appl. 35 (2015), 137–142.Search in Google Scholar

[8] Zhang, W.—Wang, T: A note on the Dirichlet characters of polynomials, Math. Slovaca 64 (2014), 301–310.Search in Google Scholar

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