Rachita Guria

collaborators

4 papers

math.NT2026

Distribution of integer points on determinant surfaces and a $mod- p$ analogue

Satadal Ganguly, Rachita Guria

We establish an asymptotic formula for counting integer solutions with smooth weights to an equation of the form $x y - z w = r$ , where $r$ is a non-zero integer, with an explicit main t…

math.NT2026

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

Satadal Ganguly, Rachita Guria

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…

math.NT2024

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

Rachita Guria

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_1…

math.NT2024

Counting $2 \times 2$ integer matrices with fixed trace and determinant

Rachita Guria

We count with a smooth weight the number of $2 \times 2$ integer matrices with a fixed characteristic polynomial with a main term and an error term using bounds for sums of Weyl su…

Distribution of integer points on determinant surfaces and a mod-p analogue

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

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

Counting 2×2 integer matrices with fixed trace and determinant

Distribution of integer points on determinant surfaces and a $mod- p$ analogue

Counting $2 \times 2$ integer matrices with fixed trace and determinant