Distribution of modular inverses and multiples of small integers and the Sato--Tate conjecture on average
| dc.creator | Shparlinski, I. E. | |
| dc.date | 2006-08-24 | |
| dc.date | 2006-11-09 | |
| dc.date.accessioned | 2026-07-07T07:22:07Z | |
| dc.date.available | 2026-07-07T07:22:07Z | |
| dc.description | We show that, for sufficiently large integers $m$ and $X$, for almost all $a =1, ..., m$ the ratios $a/x$ and the products $ax$, where $|x|\le X$, are very uniformly distributed in the residue ring modulo $m$. This extends some recent results of Garaev and Karatsuba. We apply this result to show that on average over $r$ and $s$, ranging over relatively short intervals, the distribution of Kloosterman sums $$ K_{r,s}(p) = \sum_{x=1}^{p-1} \exp(2 πi (rn + sn^{-1})/p), $$ for primes $p\le T$ is in accordance with the Sato--Tate conjecture. | |
| dc.identifier | https://arxiv.org/abs/math/0608596 | |
| dc.identifier | http://arxiv.org/abs/math/0608596 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/115541 | |
| dc.subject | Number Theory | |
| dc.subject | 11A07, 11K38, 11L05 | |
| dc.title | Distribution of modular inverses and multiples of small integers and the Sato--Tate conjecture on average | |
| dc.type | text |