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

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Showing 2020Show all

4 papers · 1 filter

math.NT2020

Diameter free estimates for the quadratic Vinogradov mean value theorem

Akshat Mudgal

Let $s \geq 3$ be a natural number, let $ψ (x)$ be a polynomial with real coefficients and degree $d \geq 2$ , and let $A$ be some large, non-empty, finite subset of real numbers. We…

math.CO2020★ 3 cited

Difference sets in higher dimensions

Akshat Mudgal

Let $d \geq 3$ be a natural number. We show that for all finite, non-empty sets $A \subseteq R^{d}$ that are not contained in a translate of a hyperplane, we have \[ |A-A| \…

math.CO2020

Sum-product estimates for diagonal matrices

Akshat Mudgal

Given $d \in N$ , we establish sum-product estimates for finite, non-empty subsets of $R^{d}$ . This is equivalent to a sum-product result for sets of diagonal matric…

math.CO2020

Arithmetic Combinatorics on Vinogradov systems

Akshat Mudgal

In this paper, we present a variant of the Balog-Szemerédi-Gowers theorem for the Vinogradov system. We then use our result to deduce a higher degree analogue of the sum-product ph…