Jump to ContentJump to Main Navigation

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year

IMPACT FACTOR increased in 2014: 1.432
Rank 22 out of 310 in category Mathematics in the 2014 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2014: 3.585
Source Normalized Impact per Paper (SNIP) 2014: 1.745
Impact per Publication (IPP) 2014: 1.262

Mathematical Citation Quotient (MCQ) 2014: 1.27



Exponential sums and congruences with factorials

Moubariz Z. Garaev1 / Florian Luca2 / Igor E. Shparlinski3




Citation Information: Journal für die reine und angewandte Mathematik. Volume 2005, Issue 584, Pages 29–44, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: 10.1515/crll.2005.2005.584.29, November 2005

Publication History

12. März 2004
Published Online:


We estimate the number of solutions of certain diagonal congruences involving factorials. We use these results to bound exponential sums with products of two factorials n!m! and also derive asymptotic formulas for the number of solutions of various congruences with factorials. For example, we prove that the products of two factorials n !m ! with max{n,m } < p 1/2+ ε are uniformly distributed modulo p, and that any residue class modulo p is representable in the form m !n ! + n 1! + …+ n 47! with max{mnn 1, … , n 47} < p 1350/1351+ ε .

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Moubariz Z. Garaev, Florian Luca, and Igor E. Shparlinski
Journal of Combinatorial Theory, Series A, 2006, Volume 113, Number 5, Page 851
Moubariz Z. Garaev, Florian Luca, and Igor E. Shparlinski
Indagationes Mathematicae, 2007, Volume 18, Number 1, Page 23
Yan Li, Min-Soo Kim, and Su Hu
Indagationes Mathematicae, 2012, Volume 23, Number 1-2, Page 19

Comments (0)

Please log in or register to comment.