2 citations · 6 across the 9 of their papers we have counts for
9 papers
New-type Quasirandom Groups and Applications
Thang Pham, Boqing Xue
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…
The Beginning and the Unfinished Story of the Millennium Prize Problems
Arthur Jaffe, Boqing Xue
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 stor…
Asymmetric estimates and the sum-product problems
Boqing Xue
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^\p…
On a Hilbert Space Reformulation of Riemann Hypothesis
Boqing Xue
We explore Hilbert space reformulations of Riemann Hypothesis developed by Nyman, Beurling, Báez-Duarte, et. al. with a weighted Bergman space , i.e.…
Natural Monoids and Non-commutative Arithmetics
Boqing Xue
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. T…
General divisor functions in arithmetic progressions to large moduli
Fei Wei, Boqing Xue, Yitang Zhang
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.
Rational points on cubic hypersurfaces that split off two forms
Boqing Xue, Haobo Dai
We show that if , defined over by a cubic form that splits off two forms, with , then is non-empty. The same hol…
On sums of subsets of Chen primes
Zhen Cui, Hongze Li, Boqing Xue
In this paper we show that if is a subset of Chen primes with positive relative density , then must have positive upper density at least $cαe^{-c^\prime\log(1/α)^{2/3}…
On sums of sparse prime subsets
Zhen Cui, Hongze Li, Boqing Xue
For arbitrary , if is a subset of the primes less than with cardinality with , then there exists a positive constant su…