An asymptotic formula with power-saving error term for counting prime solutions to a binary additive problem

Rachita Guria

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arXiv · 2410.10856

An asymptotic formula with power-saving error term for counting prime solutions to a binary additive problem

Rachita Guria

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Abstract

We obtain an asymptotic formula with a power-saving error term for counting the integer points $(a,b,c,d)$ in an expanding box $[-X,X]^4$ that satisfy the determinant equation $x_1x_2-x_3x_4=r$ for $r \neq 0$ with two of entries to be prime. The method involves the Poisson summation formula and the estimation for the average of the sums of the Kloosterman fractions over primes $p$.

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Rachita Guria. 2024-10-06. An asymptotic formula with power-saving error term for counting prime solutions to a binary additive problem. https://arxiv.org/abs/2410.10856

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