Geodesic
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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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 $p$.

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