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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 276, Pages 83–95 (Mi tm3369)  
This article is cited in 7 scientific papers (total in 7 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
Full-text PDF (209 kB) Citations (7)
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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).
Received in September 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 276, Pages 77–89
DOI: https://doi.org/10.1134/S0081543812010075
Bibliographic databases:
Document Type: Article
UDC: 511.33
Language: Russian
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, Trudy 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
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\pages 83--95
\publ MAIK Nauka/Interperiodica
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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