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.

Étant donnés un grand nombre premier p et une fonction rationnelle r(X) définie sur 𝔽 p =/p, on évalue la grandeur de l’ensemble x𝔽 p :r ˜(x)>r ˜(x+1), où r ˜(x) et r ˜(x+1) sont les plus petits représentants de r(x) et r(x+1) dans modulo p.

Given a large prime number p and a rational function r(X) defined over 𝔽 p =/p, we investigate the size of the set x𝔽 p :r ˜(x)>r ˜(x+1), where r ˜(x) and r ˜(x+1) denote the least positive representatives of r(x) and r(x+1) in modulo p.

@article{JTNB_2003__15_3_863_0,
     author = {Zaharescu, Alexandru},
     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},
     doi = {10.5802/jtnb.431},
     zbl = {02184629},
     mrnumber = {2142241},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.431/}
}
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. doi : 10.5802/jtnb.431. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.431/

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