Exponential Sums and Congruences with Factorials

Details Exponential Sums and Congruences with Factorials Exponential Sums and Congruences with Factorials

2004-03-24

arxiv.org/abs/math/0403424v1

Mathematics

Number Theory

21 pages

Scientific paper

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 $\max\{n,m\}..., n_{49}\} < p^{8775/8794+ \epsilon}$.

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