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pro vyhledávání: '"Xue, Boqing"'
Autor:
Pham, Thang, Xue, Boqing
In this paper, we study the distance problem in the setting of finite p-adic rings. In odd dimensions, our results are essentially sharp. In even dimensions, we clarify the conjecture and provide examples to support it. Surprisingly, compared to the
Externí odkaz:
http://arxiv.org/abs/2405.07325
Autor:
Pham, Thang, Xue, Boqing
This paper aims to introduce a more general definition of quasirandom groups and generalize several well-known results in the literature in this new setting. More precisely, let $G$ be a semi-direct product of groups and $X\subseteq G$, we provide co
Externí odkaz:
http://arxiv.org/abs/2308.01504
Autor:
Jaffe, Arthur, Xue, Boqing
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at their beginni
Externí odkaz:
http://arxiv.org/abs/2007.12473
Autor:
Xue, Boqing
We show two asymmetric estimates, one on the number of collinear triples and the other on that of solutions to $(a_1+a_2)(a_1^{\prime\prime\prime}+a_2^{\prime\prime\prime})=(a_1^\prime+a_2^\prime)(a_1^{\prime\prime}+a_2^{\prime\prime})$. As applicati
Externí odkaz:
http://arxiv.org/abs/2005.09893
Akademický článek
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Autor:
Xue, Boqing
We explore Hilbert space reformulations of Riemann Hypothesis developed by Nyman, Beurling, B\'{a}ez-Duarte, et. al. with a weighted Bergman space $\mathcal{H}=A_1^2(\mathbb{D})$, i.e., Riemann hypothesis holds if and only if the Hilbert subspace $\m
Externí odkaz:
http://arxiv.org/abs/1911.04029
Autor:
Xue, Boqing
We introduce several classes of monoids satisfying up to five axioms and establish basic theories on their arithmetics. The one satisfying all the axioms is named natural monoid. Two typical examples are 1) the monoid $\mathbb{N}$ of natural numbers
Externí odkaz:
http://arxiv.org/abs/1901.02149
We prove a result on the distribution of the general divisor functions in arithmetic progressions to smooth moduli which exceed the square root of the length.
Externí odkaz:
http://arxiv.org/abs/1512.01470
Autor:
Xue, Boqing, Dai, Haobo
We show that if $X\subseteq \mathbb{P}^{n-1}$, defined over $\mathbb{Q}$ by a cubic form that splits off two forms, with $n\geq 11$, then $X(\mathbb{Q})$ is non-empty. The same holds for an $(m_1,m_2)$-form with $m_1\geq 4$ and $m_2\geq 5$.
Externí odkaz:
http://arxiv.org/abs/1211.4215
In this paper we show that if $A$ is a subset of Chen primes with positive relative density $\alpha$, then $A+A$ must have positive upper density at least $c\alpha e^{-c^\prime\log(1/\alpha)^{2/3}(\log\log(1/\alpha))^{1/3}}$ in the natural numbers.
Externí odkaz:
http://arxiv.org/abs/1206.2471