naa a22 4500 51081154X CHVBK 20180411083444.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813010057 doi (NATIONALLICENCE)springer-10.1134/S0081543813010057 On congruences with products of variables from short intervals and applications [Elektronische Daten] [Jean Bourgain, Moubariz Garaev, Sergei Konyagin, Igor Shparlinski] We obtain upper bounds on the number of solutions to congruences of the type (x 1 + s)... (x ν + s) ≡ (y 1 + s)... (x ν + 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. Pleiades Publishing, Ltd., 2013 Bourgain Jean Institute for Advanced Study, Einstein Drive, 08540, Princeton, NJ, USA aut Garaev Moubariz Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México aut Konyagin Sergei Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut Shparlinski Igor Department of Computing, Macquarie University, 2109, Sydney, NSW, Australia aut Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 61-90 0081-5438 280:1<61 2013 280 11501 https://doi.org/10.1134/S0081543813010057 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813010057 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bourgain Jean Institute for Advanced Study, Einstein Drive, 08540, Princeton, NJ, USA aut NATIONALLICENCE 700 1- Garaev Moubariz Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58089, Morelia, Michoacán, México aut NATIONALLICENCE 700 1- Konyagin Sergei Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, 119991, Moscow, Russia aut NATIONALLICENCE 700 1- Shparlinski Igor Department of Computing, Macquarie University, 2109, Sydney, NSW, Australia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 61-90 0081-5438 280:1<61 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer