Jianya Liu

activity

20062021

most citedThe Möbius function and distal flows

50 citations · 64 across the 12 of their papers we have counts for

collaborators

Showing math.NTShow all

14 papers · 1 filter

math.NT2021

Manin's conjecture for singular cubic hypersurfaces

Jianya Liu, Tingting Wen, Jie Wu

Let S Q denote x 3 = Q(y 1 ,. .. , y m)z where Q is a primitive positive definite quadratic form in m variables with integer coefficients. This S Q ranges over a class of singular…

math.NT2021

On forms in prime variables

Jianya Liu, Lilu Zhao

Let $F_{1}, \dots, F_{R}$ be homogeneous polynomials of degree $d \geq 2$ with integer coefficients in $n$ variables, and let $F = (F_{1}, \dots, F_{R})$ . Suppose that $F_{1}, \dots, F_{R}$ …

math.NT2021

Representation by sums of unlike powers

Jianya Liu, Lilu Zhao

It is proved that all sufficiently large integers $n$ can be represented as $n = x_{1}^{2} + x_{2}^{3} + \dots + x_{13}^{14},$ where $x_{1}, \dots, x_{13}$ are positive integers. This improves upo…

math.NT2019

Gaussian primes in almost all narrow sectors

Bingrong Huang, Jianya Liu, Zeév Rudnick

We study Gaussian primes lying in narrow sectors, and show that almost all such sectors contain the expected number of primes, if the sectors are not too narrow.

math.NT2018

On a senary quartic form

Jianya Liu, Jie Wu, Yongqiang Zhao

We count rational points of bounded height on the non-normal senary quartic hypersurface x 4 = (y 2 1 + $\times$ $\times$ $\times$ + y 2 4)z 2 in the spirit of Manin's conjecture.

math.NT2017★ 1 cited

On a certain non-split cubic surface

Régis de la Bretèche, Kevin Destagnol, Jianya Liu +2

In this note, we establish an asymptotic formula for the number of rational points of bounded height on the singular cubic surface $x_{0} (x_{1}^{2} + x_{2}^{2}) = x_{3}^{3}$ with a power-savin…