Asymptotics for the sum of powers of distances between power residues modulo a~prime
Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 83-95
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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 $p$.
@article{TRSPY_2012_276_a6,
author = {M. Z. Garaev and S. V. Konyagin and Yu. V. Malykhin},
title = {Asymptotics for the sum of powers of distances between power residues modulo a~prime},
journal = {Informatics and Automation},
pages = {83--95},
publisher = {mathdoc},
volume = {276},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a6/}
}
TY - JOUR AU - M. Z. Garaev AU - S. V. Konyagin AU - Yu. V. Malykhin TI - Asymptotics for the sum of powers of distances between power residues modulo a~prime JO - Informatics and Automation PY - 2012 SP - 83 EP - 95 VL - 276 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a6/ LA - ru ID - TRSPY_2012_276_a6 ER -
%0 Journal Article %A M. Z. Garaev %A S. V. Konyagin %A Yu. V. Malykhin %T Asymptotics for the sum of powers of distances between power residues modulo a~prime %J Informatics and Automation %D 2012 %P 83-95 %V 276 %I mathdoc %U http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a6/ %G ru %F TRSPY_2012_276_a6
M. Z. Garaev; S. V. Konyagin; Yu. V. Malykhin. Asymptotics for the sum of powers of distances between power residues modulo a~prime. Informatics and Automation, Number theory, algebra, and analysis, Tome 276 (2012), pp. 83-95. http://geodesic.mathdoc.fr/item/TRSPY_2012_276_a6/