5 citations · 5 across the 1 of their papers we have counts for
4 papers
Energy estimates in sum-product and convexity problems
Akshat Mudgal
We prove a new class of low-energy decompositions which, amongst other consequences, imply that any finite set of integers may be written as , where and a…
Sum-product estimates for diagonal matrices
Akshat Mudgal
Given , we establish sum-product estimates for finite, non-empty subsets of . This is equivalent to a sum-product result for sets of diagonal matric…
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…
Sums of linear transformations in higher dimensions
Akshat Mudgal
In this paper, we prove the following two results. Let be a natural number and be co-prime integers such that . Then there exists a constant depending only…