Twisted Linnik implies optimal covering exponent for $S^3$

TL;DR

This paper demonstrates that a twisted version of Linnik's conjecture on Kloosterman sums implies the optimal covering exponent for the 3-sphere, connecting deep conjectures to geometric covering problems.

Contribution

It establishes a link between a twisted Linnik conjecture and the optimal covering exponent for $S^3$, providing new insights into the interplay between number theory and geometry.

Findings

Twisted Linnik conjecture implies optimal covering exponent for $S^3$

Connection between Kloosterman sums and geometric covering problems

Advances understanding of conjectural implications in number theory

Abstract

We show that a twisted variant of Linnik's conjecture on sums of Kloosterman sums leads to an optimal covering exponent for $S^3$.