On congruences with products of variables from short intervals and applications
By Jean Bourgain, Moubariz Z. Garaev, Sergei V. Konyagin, Igor E. Shparlinski. 2012
48 citations recorded by the source corpus.
We obtain upper bounds on the number of solutions to congruences of the type (x1 + s)... (xν + s) ≡ (y1 + s)... (xν + s) ≢ 0 (mod p) modulo a prime p with variables from some short intervals. We give some applications of our results and in particular improve several recent estimates of J. Cilleruelo and M.Z. Garaev on exponential congruences and on cardinalities of products of short intervals, some double character sum estimates of J. Friedlander and H. Iwaniec and some results of M.-C. Chang and A.A. Karatsuba on character sums twisted with the divisor function.
Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/fcf16161e72d1945ba068a1bb4fe8ae623bc6d89
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Modular hyperbolas (2011, background): “Several more related estimates are given in [12, 36, 37, 60, 61, 96].”