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Estimate of quadratic trigonometric sums with prime numbers

Authors:	F. Z. Rakhmonov

Affiliation:	1.Faculty of Mechanics and Mathematics,Moscow State University,Leninskie Gory, Moscow,Russia

Abstract:	An estimate of the modulus of an exponential sum over primes $S_2 left( {alpha ;x,1} right) = sumlimits_{n leqslant x} {Lambda left( n right)eleft( {alpha left( {n + 1} right)^2 } right)}$ is obtained, where α is approximated by a rational number with a large denominator.

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