Uniform Distribution of Fractional Parts Related to Pseudoprimes
| dc.creator | Banks, William D. | |
| dc.creator | Garaev, Moubariz Z. | |
| dc.creator | Luca, Florian | |
| dc.creator | Shparlinski, Igor E. | |
| dc.date | 2005-05-05 | |
| dc.date | 2005-08-06 | |
| dc.date.accessioned | 2026-07-07T05:19:40Z | |
| dc.date.available | 2026-07-07T05:19:40Z | |
| dc.description | We estimate exponential sums with the Fermat-like quotients $$ f_g(n) = \frac{g^{n-1} - 1}{n} \mand h_g(n)=\frac{g^{n-1}-1}{P(n)}, $$ where $g$ and $n$ are positive integers, $n$ is composite, and P(n) is the largest prime factor of $n$. Clearly, both $f_g(n)$ and $h_g(n)$ are integers if $n$ is a Fermat pseudoprime to base $g$, and if $n$ is a Carmichael number this is true for all $g$ coprime to $n$. Nevertheless, our bounds imply that the fractional parts $\{f_g(n)\}$ and $\{h_g(n)\}$ are uniformly distributed, on average over $g$ for $f_g(n)$, and individually for $h_g(n)$. We also obtain similar results with the functions ${\widetilde f}_g(n) = gf_g(n)$ and ${\widetilde h}_g(n) = gh_g(n)$. | |
| dc.description | In the new version we use an idea of Moubariz Garaev (who is now a co-author) to improve some of the results of the previous version | |
| dc.identifier | https://arxiv.org/abs/math/0505098 | |
| dc.identifier | http://arxiv.org/abs/math/0505098 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/75099 | |
| dc.subject | Number Theory | |
| dc.subject | 11L07, 11N37, 11N60 | |
| dc.title | Uniform Distribution of Fractional Parts Related to Pseudoprimes | |
| dc.type | text |