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 Tr. Mat. Inst. Steklova, 2012, Volume 276, Pages 83–95 (Mi tm3369)

Asymptotics for the sum of powers of distances between power residues modulo a prime

M. Z. Garaeva, S. V. Konyaginb, Yu. V. Malykhinb

a Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, Michoacán, México
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

Abstract: For fixed $q\in(0,4)$, prime $p\to\infty$, and $d\le\exp(c\sqrt{\ln p})$, where $c>0$ is a constant, we obtain the asymptotics for the sum of $q$th powers of distances between neighboring residues of degree $d$ modulo $p$.

 Funding Agency Grant Number Russian Foundation for Basic Research 11-01-00329 Ministry of Education and Science of the Russian Federation NSh-65772.2010.1 The second and third authors were supported by the Russian Foundation for Basic Research ( project no. 11-01-00329), and the third author was also supported by a grant of the President of the Russian Federation ( project no. NSh-65772.2010.1).

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 276, 77–89

Bibliographic databases:

Document Type: Article
UDC: 511.33

Citation: M. Z. Garaev, S. V. Konyagin, Yu. V. Malykhin, “Asymptotics for the sum of powers of distances between power residues modulo a prime”, Number theory, algebra, and analysis, Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday, Tr. Mat. Inst. Steklova, 276, MAIK Nauka/Interperiodica, Moscow, 2012, 83–95; Proc. Steklov Inst. Math., 276 (2012), 77–89

Citation in format AMSBIB
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This publication is cited in the following articles:
1. D. E. Kovalevskii, “Otsenka summy stepenei rasstoyanii mezhdu vychetami po prostomu modulyu”, Chebyshevskii sb., 13:2 (2012), 77–85
2. Dietmann R., Elsholtz Ch., Shparlinski I.E., “On Gaps Between Quadratic Non-Residues in the Euclidean and Hamming Metrics”, Indag. Math.-New Ser., 24:4, SI (2013), 930–938
3. Konyagin S.V., Shparlinski I.E., “Quadratic Non-Residues in Short Intervals”, Proc. Amer. Math. Soc., 143:10 (2015), 4261–4269
4. Shparlinski I.E., “On small gaps between the elements of multiplicative subgroups of finite fields”, Des. Codes Cryptogr., 80:1 (2016), 63–71
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