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Rachita Guria

Publications and source records attributed to Rachita Guria.

4 recordsLinked to original sources
arXiv2026

Prime Solutions to a Binary Additive Equation and Mixed Moments of Character Sums

We obtain an asymptotic formula with a power-saving error term for counting the integer points $(a,b,c,d)$ in an expanding box that satisfy the determinant equation $x_1x_2-x_3x_4 =r$ for $r \neq 0 $ with two of entries to be prime. Finally, these estimates are applied to evaluate mixed fourth moments of Dirichlet character sums over integers and primes, yielding non-trivial bounds. The method involves the Poisson summation formula and the estimation for the average of the sums of the Kloosterman fractions over primes.

math.NT↗
arXiv2026

Lattice points on determinant surfaces and the spectrum of the automorphic Laplacian

We use classical Fourier analysis along with tools from the spectral theory of Automorphic forms to derive an asymptotic formula with a strong error term for the number of integer solutions $(a, b, c, d)$ inside the expanding box $[-X,X]^4$ to the determinant equation $ad-bc=r$, where $r \neq 0$ is a fixed integer. Furthermore, we apply our method to study sums over these solutions where the variables are weighted by periodic arithmetical functions in two of the variables in one case, and by an arbitrary sequence of complex numbers in another.

math.NT↗
arXiv2026

Distribution of integer points on determinant surfaces and a $\text{mod-}p$ analogue

We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $xy-zw=r$, where $r$ is a non-zero integer, with an explicit main term and a strong bound on the error term in terms of the size of the variables $x, y, z, w$ as well as of $r$. We also establish an asymptotic formula for counting integer solutions with smooth weights to the congruence $xy-zw \equiv 1 (\text{mod }p)$, where $p$ is a large prime, with a strong bound on the error term.

math.NT↗