Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Kumchev, Angel V."'
We decompose the discrete bilinear spherical averaging operator into simpler operators in several ways. This leads to a wide array of extensions, such as to the simplex averaging operator, and applications, such as to operator bounds.
Externí odkaz:
http://arxiv.org/abs/2305.14346
Autor:
Carneiro, Emanuel, Das, Mithun Kumar, Florea, Alexandra, Kumchev, Angel V., Malik, Amita, Milinovich, Micah B., Turnage-Butterbaugh, Caroline, Wang, Jiuya
Publikováno v:
J. Funct. Anal. 281 (2021), no. 9, Paper No. 109199
We improve the current bounds for an inequality of Erd\H{o}s and Tur\'an from 1950 related to the discrepancy of angular equidistribution of the zeros of a given polynomial. Building upon a recent work of Soundararajan, we establish a novel connectio
Externí odkaz:
http://arxiv.org/abs/2104.00105
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research. Here we un
Externí odkaz:
http://arxiv.org/abs/2006.09968
Autor:
Kumchev, Angel V., Wooley, Trevor D.
Publikováno v:
Monatsh. Math. 183, 303-310 (2017)
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 $k \ge 7$, and in particular establish that for large $k$ one has \[H(k)\le
Externí odkaz:
http://arxiv.org/abs/1602.08592
Autor:
Kumchev, Angel V., Wooley, Trevor D.
Publikováno v:
J. London Math. Soc. 93 (2016), 811-824
Recent progress on Vinogradov's mean value theorem has resulted in improved estimates for exponential sums of Weyl type. We apply these new estimates to obtain sharper bounds for the function $H(k)$ in the Waring--Goldbach problem. We obtain new resu
Externí odkaz:
http://arxiv.org/abs/1510.00982
Autor:
Kumchev, Angel V., Zhao, Lilu
Publikováno v:
Mathematika 62 (2016) 348-361
Let $E(N)$ denote the number of positive integers $n \le N$, with $n \equiv 4 \pmod{24}$, which cannot be represented as the sum of four squares of primes. We establish that $E(N)\ll N^{11/32}$, thus improving on an earlier result of Harman and the f
Externí odkaz:
http://arxiv.org/abs/1503.01799
Autor:
Kumchev, Angel V.
The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.
Externí odkaz:
http://arxiv.org/abs/1112.0201
Autor:
Kumchev, Angel V.
Publikováno v:
Ramanujan J. 30 (2013), 101-116
We study the convergence sets of a class of alternating series. Among other things, our results establish the convergence of the series $\sum_n (-1)^n|\sin n|/n$.
Externí odkaz:
http://arxiv.org/abs/1102.4644
Autor:
Chan, Tsz Ho, Kumchev, Angel V
Publikováno v:
Acta Arith. 152 (2012), 1-10
Let $c_q(n)$ denote the Ramanujan sum modulo $q$, and let $x$ and $y$ be large reals, with $x = o(y)$. We obtain asymptotic formulas for the sums $$\sum_{n \le y}(\sum_{q \le x} c_q(n))^k \qquad (k = 1, 2).$$
Externí odkaz:
http://arxiv.org/abs/1009.4432
Publikováno v:
International Journal of Number Theory; Apr2024, Vol. 20 Issue 3, p867-892, 26p
