The distribution of the values of a rational function modulo a big prime

Alexandru Zaharescu

Alexandru Zaharescu

Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 863-872.

Résumé
Abstract

Étant donnés un grand nombre premier $p$ et une fonction rationnelle $r (X)$ définie sur $𝔽_{p} = ℤ / p ℤ$ , on évalue la grandeur de l’ensemble $\{x \in 𝔽_{p} : \tilde{r} (x) > \tilde{r} (x + 1)\}$ , où $\tilde{r} (x)$ et $\tilde{r} (x + 1)$ sont les plus petits représentants de $r (x)$ et $r (x + 1)$ dans $ℤ$ modulo $p ℤ$ .

Given a large prime number $p$ and a rational function $r (X)$ defined over $𝔽_{p} = ℤ / p ℤ$ , we investigate the size of the set $\{x \in 𝔽_{p} : \tilde{r} (x) > \tilde{r} (x + 1)$ , where $\tilde{r} (x)$ and $\tilde{r} (x + 1)$ denote the least positive representatives of $r (x)$ and $r (x + 1)$ in $ℤ$ modulo $p ℤ$ .

MR Zbl

@article{JTNB_2003__15_3_863_0,
     author = {Alexandru Zaharescu},
     title = {The distribution of the values of a rational function modulo a big prime},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     pages = {863--872},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {3},
     year = {2003},
     zbl = {02184629},
     mrnumber = {2142241},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2003__15_3_863_0/}
}

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Alexandru Zaharescu. The distribution of the values of a rational function modulo a big prime. Journal de théorie des nombres de Bordeaux, Tome 15 (2003) no. 3, pp. 863-872. https://jtnb.centre-mersenne.org/item/JTNB_2003__15_3_863_0/

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