A. Kumchev

activity

20042023

most citedAdditive representation in short intervals, II: sums of two like powers

24 citations · 91 across the 21 of their papers we have counts for

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math.NT2023

Short Interval Results For Powerfree Polynomials Over Finite Fields

Angel Kumchev, Nathan McNew, Ariana Park

Let $k \geq 2$ be an integer and $F_{q}$ be a finite field with $q$ elements. We prove several results on the distribution in short intervals of polynomials in $\mathbb F_q[x…

math.NT2022

Explicit bounds for large gaps between squarefree integers

Angel Kumchev, Wade McCormick, Nathan McNew +3

We obtain explicit forms of the current best known asymptotic upper bounds for gaps between squarefree integers. In particular we show, for any $x \geq 2$ , that every interval of th…

math.NT2020

Discrete maximal operators over surfaces of higher codimension

Theresa C. Anderson, Eyvindur Ari Palsson, Angel V. Kumchev

Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analy…

math.NT2018

A hybrid of two theorems of Piatetski-Shapiro

Angel Kumchev, Zhivko Petrov

Let $c > 1$ and $0 < γ < 1$ be real, with $c \in / N$ . We study the solubility of the Diophantine inequality \[ \left| p_1^c + p_2^c + \dots + p_s^c - N \right| < \varepsil…

math.NT2016

On sums of powers of almost equal primes

Angel Kumchev, Huafeng Liu

Let $k \geq 2$ and $s$ be positive integers, and let $n$ be a large positive integer subject to certain local conditions. We prove that if $s \geq k^{2} + k + 1$ and $θ > 31/40$ , then $n$ c…

math.NT2016

On the Waring-Goldbach problem for seventh and higher powers

Angel V. Kumchev, Trevor D. Wooley

We apply recent progress on Vinogradov's mean value theorem to improve bounds for the function $H (k)$ in the Waring-Goldbach problem. We obtain new results for all exponents $k \ge…