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}, mrnumber = {2152216}, zbl = {1101.11027}, 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 DA - 2005/// SP - 151 EP - 160 VL - 17 IS - 1 PB - Université Bordeaux 1 UR - http://www.numdam.org/articles/10.5802/jtnb.482/ UR - https://www.ams.org/mathscinet-getitem?mr=2152216 UR - https://zbmath.org/?q=an%3A1101.11027 UR - https://doi.org/10.5802/jtnb.482 DO - 10.5802/jtnb.482 LA - en ID - JTNB_2005__17_1_151_0 ER -
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 2142292 | Zbl 02195395
[2] D. A. Burgess, On character sums and -series, II. Proc. London Math. Soc. (3) 13 (1963), 524–536. | MR 148626 | Zbl 0123.04404
[3] M. Z. Garaev, F. Luca, I. E. Shparlinski, Character sums and congruences with . Trans. Amer. Math. Soc. 356 (2004), 5089–5102. | MR 2084412 | Zbl 1060.11046
[4] M. Z. Garaev, F. Luca, I. E. Shparlinski, Exponential sums and congruences with factorials. J. reine angew. Math., to appear. | MR 2155084 | Zbl 1071.11051
[5] M. Z. Garaev, F. Luca, I. E. Shparlinski, Waring problem with factorials mod . Bull. Australian Math. Soc. 71 (2005), 259–264. | MR 2133409 | Zbl 1076.11013
[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 269611 | Zbl 0224.10043
[7] F. Luca, P. Stănică, Products of factorials modulo . Colloq. Math. 96 no. 2 (2003), 191–205. | MR 2010354 | Zbl 1042.11002
[8] A. Sárkőzy, On the distribution of residues of products of integers. Acta Math. Hung. 49 (3-4) (1987), 397–401. | MR 891052 | Zbl 0629.10004
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