Akshat Mudgal

activity

20192026

most citedEnergy estimates in sum-product and convexity problems

5 citations · 9 across the 22 of their papers we have counts for

collaborators

Showing 2023Show all

4 papers · 1 filter

math.NT2023

A Quadratic Vinogradov Mean Value Theorem in Finite Fields

Samuel Mansfield, Akshat Mudgal

Let $p$ be a prime, let $s \geq 3$ be a natural number and let $A \subseteq F_{p}$ be a non-empty set satisfying $∣ A ∣ ≪ p^{1/2}$ . Denoting $J_{s} (A)$ to be the number of sol…

math.CO2023

An Elekes-Rónyai theorem for sets with few products

Akshat Mudgal

Given $d, n \in N$ , we write a polynomial $F \in C [x_{1}, \dots, x_{n}]$ to be degenerate if there exist $P \in C [y_{1}, \dots, y_{n - 1}]$ and $m_j = x_1^{v_{j,1}}\…

math.CO2023

Kemperman's inequality and Freiman's lemma via few translates

Yifan Jing, Akshat Mudgal

Let $G$ be a connected compact group equipped with the normalised Haar measure $μ$ . Our first result shows that given $α, β > 0$ , there is a constant $c = c (α, β) > 0$ such that for any…

math.NT2023

Unbounded expansion of polynomials and products

Akshat Mudgal

Given $d, s \in N$ , a finite set $A \subseteq Z$ and polynomials $φ_{1}, \dots, φ_{s} \in Z [x]$ such that $1 \leq d e g φ_{i} \leq d$ for every $1 \leq i \leq s…