Dans cet article, on utilise des estimations de sommes de charactères pour étudier les produits de factorielles modulo .
In this paper, we apply character sum estimates to study products of factorials modulo .
@article{JTNB_2005__17_1_151_0,
author = {Garaev, Moubariz Z. and Luca, Florian},
title = {Character sums and products of factorials modulo $p$},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {151--160},
publisher = {Universit\'e Bordeaux 1},
volume = {17},
number = {1},
year = {2005},
doi = {10.5802/jtnb.482},
zbl = {1101.11027},
mrnumber = {2152216},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jtnb.482/}
}
TY - JOUR AU - Garaev, Moubariz Z. AU - Luca, Florian TI - Character sums and products of factorials modulo $p$ JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 151 EP - 160 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.482/ DO - 10.5802/jtnb.482 LA - en ID - JTNB_2005__17_1_151_0 ER -
%0 Journal Article %A Garaev, Moubariz Z. %A Luca, Florian %T Character sums and products of factorials modulo $p$ %J Journal de théorie des nombres de Bordeaux %D 2005 %P 151-160 %V 17 %N 1 %I Université Bordeaux 1 %U http://www.numdam.org/articles/10.5802/jtnb.482/ %R 10.5802/jtnb.482 %G en %F JTNB_2005__17_1_151_0
Garaev, Moubariz Z.; Luca, Florian. Character sums and products of factorials modulo $p$. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 1, pp. 151-160. doi : 10.5802/jtnb.482. http://www.numdam.org/articles/10.5802/jtnb.482/
[1] W. Banks, F. Luca, I. E. Shparlinski, H. Stichtenoth, On the value set of modulo a prime. Turkish J. Math. 29 no. 2 (2005), 169–174. | MR | Zbl
[2] D. A. Burgess, On character sums and -series, II. Proc. London Math. Soc. (3) 13 (1963), 524–536. | MR | Zbl
[3] M. Z. Garaev, F. Luca, I. E. Shparlinski, Character sums and congruences with . Trans. Amer. Math. Soc. 356 (2004), 5089–5102. | MR | Zbl
[4] M. Z. Garaev, F. Luca, I. E. Shparlinski, Exponential sums and congruences with factorials. J. reine angew. Math., to appear. | MR | Zbl
[5] M. Z. Garaev, F. Luca, I. E. Shparlinski, Waring problem with factorials mod . Bull. Australian Math. Soc. 71 (2005), 259–264. | MR | Zbl
[6] A. A. Karatsuba, The distribution of products of shifted prime numbers in arithmetic progressions. Dokl. Akad. Nauk SSSR 192 (1970), 724–727 (in Russian). | MR | Zbl
[7] F. Luca, P. Stănică, Products of factorials modulo . Colloq. Math. 96 no. 2 (2003), 191–205. | MR | Zbl
[8] A. Sárkőzy, On the distribution of residues of products of integers. Acta Math. Hung. 49 (3-4) (1987), 397–401. | MR | Zbl
Cité par Sources :
