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

• Volume: 15, Issue: 3, page 863-872
• ISSN: 1246-7405

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## Abstract

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

## How to cite

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Zaharescu, Alexandru. "The distribution of the values of a rational function modulo a big prime." Journal de théorie des nombres de Bordeaux 15.3 (2003): 863-872. <http://eudml.org/doc/249072>.

@article{Zaharescu2003,
abstract = {Given a large prime number $p$ and a rational function $r(X)$ defined over $\mathbb \{F\}_p = \mathbb \{Z\} / p \mathbb \{Z\}$, we investigate the size of the set $\left\lbrace x \in \mathbb \{F\}_p : \tilde\{r\}(x) &gt; \tilde\{r\}(x +1)\right.$, where $\tilde\{r\}(x)$ and $\tilde\{r\}(x + 1)$ denote the least positive representatives of $r(x)$ and $r(x+1)$ in $\mathbb \{Z\}$ modulo $p\mathbb \{Z\}$.},
author = {Zaharescu, Alexandru},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {rational function; distribution of values},
language = {eng},
number = {3},
pages = {863-872},
publisher = {Université Bordeaux I},
title = {The distribution of the values of a rational function modulo a big prime},
url = {http://eudml.org/doc/249072},
volume = {15},
year = {2003},
}

TY - JOUR
AU - Zaharescu, Alexandru
TI - The distribution of the values of a rational function modulo a big prime
JO - Journal de théorie des nombres de Bordeaux
PY - 2003
PB - Université Bordeaux I
VL - 15
IS - 3
SP - 863
EP - 872
AB - Given a large prime number $p$ and a rational function $r(X)$ defined over $\mathbb {F}_p = \mathbb {Z} / p \mathbb {Z}$, we investigate the size of the set $\left\lbrace x \in \mathbb {F}_p : \tilde{r}(x) &gt; \tilde{r}(x +1)\right.$, where $\tilde{r}(x)$ and $\tilde{r}(x + 1)$ denote the least positive representatives of $r(x)$ and $r(x+1)$ in $\mathbb {Z}$ modulo $p\mathbb {Z}$.
LA - eng
KW - rational function; distribution of values
UR - http://eudml.org/doc/249072
ER -

## References

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