On character sums and the exceptional set of a congruence problem |
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| Authors: | M.Z. Garaev A.A. Karatsuba |
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| Affiliation: | a Instituto de Matemáticas UNAM, Campus Morelia, Ap. Postal 61-3 (Xangari), CP 58089, Morelia, Michoacán, México
b Steklov Institute of Mathematics, Russian Academy of Sciences, GSP-1, UL. Gubkina 8, Moscow, Russian Federation |
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| Abstract: | We prove an estimate of character sums. This bound and the method of solving multiplicative ternary problems are used to obtain new results about the cardinality of an exceptional set of a congruence problem modulo a prime p. In particular, we show that “almost all” residue classes modulo p are representable in the form  , where  |
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| Keywords: | 11A07 11L40 |
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