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

This article is cited in 4 scientific papers (total in 4 papers)

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:

UDC: 511.33
Received in September 2011

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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\paper Asymptotics for the sum of powers of distances between power residues modulo a~prime
\inbook Number theory, algebra, and analysis
\bookinfo Collected papers. Dedicated to Professor Anatolii Alekseevich Karatsuba on the occasion of his 75th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 276
\pages 83--95
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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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  mathnet
    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  crossref  mathscinet  zmath  isi
    3. Konyagin S.V., Shparlinski I.E., “Quadratic Non-Residues in Short Intervals”, Proc. Amer. Math. Soc., 143:10 (2015), 4261–4269  crossref  mathscinet  zmath  isi  elib
    4. Shparlinski I.E., “On small gaps between the elements of multiplicative subgroups of finite fields”, Des. Codes Cryptogr., 80:1 (2016), 63–71  crossref  mathscinet  zmath  isi  elib  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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