ENERGY BOUNDS FOR MODULAR ROOTS AND THEIR APPLICATIONS

Bryce Kerr, Ilya D. Shkredov, Igor E. Shparlinski, Alexandru Zaharescu

Type: Article

Publication Date: 2024-03-04

Citations: 4

DOI: https://doi.org/10.1017/s1474748023000397

Abstract

Abstract We generalise and improve some recent bounds for additive energies of modular roots. Our arguments use a variety of techniques, including those from additive combinatorics, algebraic number theory and the geometry of numbers. We give applications of these results to new bounds on correlations between Salié sums and to a new equidistribution estimate for the set of modular roots of primes.

Locations

Journal of the Institute of Mathematics of Jussieu - View - PDF
arXiv (Cornell University) - View - PDF
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+	Об энергии корней	2024	Aleksei Volostnov
+	Lattices in function fields and applications	2025	Christian Bagshaw Bryce Kerr

Works Cited by This (29)

Action	Title	Year	Authors
+	Gauss and Jacobi sums	1998	Bruce C. Berndt Kenneth S. Williams Ronald J. Evans
+	Some Applications of Modular Forms	1990	Peter Sarnak
+	An Introduction to the Geometry of Numbers	1959	J. W. S. Cassels
+	Energies and structure of additive sets	2014	Ilya D. Shkredov
+ PDF Chat	Successive-minima-type inequalities	1993	U. Betke Martin Henk J. M. Wills
+ PDF Chat	On congruences with products of variables from short intervals and applications	2013	Jean Bourgain Moubariz Z. Garaev Sergeĭ Konyagin Igor E. Shparlinski
+	On the Linear Independence of Fractional Powers of Integers	1940	A. S. Besicovitch
+ PDF Chat	On multiple Salié sums	1992	William Duke
+	Incomplete Kloosterman Sums and a Divisor Problem	1985	John Friedlander Henryk Iwaniec
+	The Congruencex1x2≡x3x4(modp), the Equationx1x2≡x3x4, and Mean Values of Character Sums	1996	Anwar Ayyad Todd Cochrane Zhiyong Zheng