Abstract:
In the paper we prove a new upper bound for Heilbronn's exponential sum and obtain some applications of our result to a distribution of Fermat quotients.
This work was supported by grant RFFI NN 06-01-00383, 11-01-00759, Russian Government project 11.G34.31.0053, Federal Program 'Scientific and scientific-pedagogical staff of innovative Russia' 2009-2013 and grant Leading Scientific Schools N 2519.2012.1.
Received: 14.12.2012
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Article
Language: English
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https://www.mathnet.ru/eng/qjm3
This publication is cited in the following 9 articles:
Stephan Ramon Garcia, Foundations for Undergraduate Research in Mathematics, A Project-Based Guide to Undergraduate Research in Mathematics, 2020, 203
Stephan Ramon Garcia, Bob Lutz, “A supercharacter approach to Heilbronn sums”, Journal of Number Theory, 186 (2018), 1
I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “On the Additive Energy of the Heilbronn Subgroup”, Math. Notes, 101:1 (2017), 58–70
Todd Cochrane, Dilum De Silva, Christopher Pinner, “(p - 1)th Roots of unity mod pn, generalized Heilbronn sums, Lind-Lehmer constants, and Fermat quotients”, Michigan Math. J., 66:1 (2017)
Igor E. Shparlinski, “Ratios of Small Integers in Multiplicative Subgroups of Residue Rings”, Experimental Mathematics, 25:3 (2016), 273
Glyn Harman, Igor E. Shparlinski, “Products of Small Integers in Residue Classes and Additive Properties of Fermat Quotients”, Int Math Res Notices, 2016:5 (2016), 1424
Yu. N. Shteinikov, “Estimates of Trigonometric Sums over Subgroups and Some of Their Applications”, Math. Notes, 98:4 (2015), 667–684
I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163
ZhiXiong Chen, “Trace representation and linear complexity of binary sequences derived from Fermat quotients”, Sci. China Inf. Sci., 57:11 (2014), 1
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