Akshat Mudgal

collaborators

9 papers

math.NT2026

On an asymmetric additive energy inequality

Akshat Mudgal

Let $d \geq 1$ be an integer, $G$ be an abelian group and $I^½, w_{1}, \dots, w_{2 d} : G \to [0, \infty)$ be functions with finite, non-empty supports. Define the generalised additive…

math.NT2026

Counting $2 \times 2$ integer matrices with a given determinant

Jonathan Chapman, Akshat Mudgal

Given positive integers $h, N$ satisfying $1 ⩽ h ⩽ 2 N^{2}$ , we define $T (h, N)$ to be the number of $2 \times 2$ integer matrices with determinant equal to $h$ whose en…

math.NT2026

Counting solutions to the quadratic determinant equation

Jonathan Chapman, Akshat Mudgal

Given $h, N \in N$ satisfying $1 ⩽ h ⩽ N^{2}$ , we prove an asymptotic formula for the number of solutions to the equation $x_{1} x_{2} - x_{3} x_{4} = h$ with $x_1,…

math.NT2026

A structure theorem for sets with doubling $4 + I^´$

Yifan Jing, Akshat Mudgal

We prove a structural result for sets of integers with doubling at most $4 + I^´$ , with $I^´ > 0$ sufficiently small. This generalises earlier work of Eberhard--Green--Manners which de…

math.NT2026

Uniform sum-product phenomenon for algebraic groups and Bremner's conjecture

Joseph Harrison, Akshat Mudgal, Harry Schmidt

In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this…

math.NT2025

Generalised Fermat equations in dense variables over finite fields and rings

Sam Chow, Zi Li Lim, Akshat Mudgal

Let $A$ be a sufficiently dense subset of a finite field $F_{q}$ or a finite, cyclic ring $Z / N Z$ . Assuming that $q$ and $N$ have no small prime divisors, we…

On an asymmetric additive energy inequality

Counting 2×2 integer matrices with a given determinant

Counting solutions to the quadratic determinant equation

A structure theorem for sets with doubling 4+I^´

Uniform sum-product phenomenon for algebraic groups and Bremner's conjecture

Generalised Fermat equations in dense variables over finite fields and rings

Counting $2 \times 2$ integer matrices with a given determinant

A structure theorem for sets with doubling $4 + I^´$