Junxian Li

activity

20162025

most citedLower bounds for discrete negative moments of the Riemann zeta function

12 citations · 31 across the 17 of their papers we have counts for

collaborators

17 papers

quant-ph2025

Partial transpose as a space-time swap

James Fullwood, Junxian Li

While the partial transpose operation appears in many fundamental results in quantum theory -- such as the Peres-Horodecki criterion for entanglement detection -- a physical interp…

math.NT2024

Level aspect subconvexity for $GL(2) \times GL(2)$ $L$ -functions

Keshav Aggarwal, Sumit Kumar, Chung-Hang Kwan +3

Let $f$ be a newform of prime level $p$ with any central character $χ (mod p)$ , and let $g$ be a fixed cusp form or Eisenstein series for $SL_{2} (Z)$ . We prov…

gr-qc2023★ 2 cited

Corrections to the thermodynamic quantities of Bose system by the generalized uncertainty principle

Jun-Xian Li, Jing-Yi Zhang

This paper investigated the Bose system in a spherical shell close to the black hole horizon. Several thermodynamic quantities of the Bose system are derived, which are different f…

math.NT2023

Simultaneous extreme values of zeta and L-functions

Winston Heap, Junxian Li

We show that distinct primitive L-functions can achieve extreme values simultaneously on the critical line. Our proof uses a modification of the resonance method and can be applied…

math.NT2022

Correlations of values of random diagonal forms

Valentin Blomer, Junxian Li

We study the value distribution of diagonal forms in k variables and degree d with random real coefficients and positive integer variables, normalized so that mean spacing is one.…

math.NT2022

Simultaneous large values and dependence of Dirichlet $L$ -functions in the critical strip

Shōta Inoue, Junxian Li

We consider the joint value distribution of Dirichlet $L$ -functions in the critical strip $\frac{1}{2} < σ < 1$ . We show that the values of distinct Dirichlet $L$ -functions are depe…

math.NT2021

Additive problems with almost prime squares

Valentin Blomer, Lasse Grimmelt, Junxian Li +1

We show that every sufficiently large integer is a sum of a prime and two almost prime squares, and also a sum of a smooth number and two almost prime squares. The number of such r…

math.NT2021★ 1 cited

Joint value distribution of $L$ -functions on the critical line

Shōta Inoue, Junxian Li

In this paper, we discuss the joint value distribution of $L$ -functions in a suitable class. We obtain joint large deviations results in the central limit theorem for these $L$ -fun…

math.NT2020★ 2 cited

Uniform Titchmarsh divisor problems

Edgar Assing, Valentin Blomer, Junxian Li

Asymptotic formulae for Titchmarsh-type divisor sums are obtained with strong error terms that are uniform in the shift parameter. This applies to more general arithmetic functions…

math.NT2020★ 12 cited

Lower bounds for discrete negative moments of the Riemann zeta function

Winston Heap, Junxian Li, Jing Zhao

We prove lower bounds for the discrete negative $2 k$ th moment of the derivative of the Riemann zeta function for all fractional $k ⩾ 0$ . The bounds are in line with a conjec…

math.PR2019★ 6 cited

The Surprising Accuracy of Benford's Law in Mathematics

Zhaodong Cai, Matthew Faust, A. J. Hildebrand +2

Benford's law is an empirical ``law'' governing the frequency of leading digits in numerical data sets. Surprisingly, for mathematical sequences the predictions derived from it can…

math.NT2018★ 1 cited

A local Benford Law for a class of arithmetic sequences

Zhaodong Cai, A. J. Hildebrand, Junxian Li

It is well-known that sequences such as the Fibonacci numbers and the factorials satisfy Benford's Law, that is, leading digits in these sequences occur with frequencies given by $…

math.NT2018

Almost Beatty Partitions

A. J. Hildebrand, Junxian Li, Xiaomin Li +1

Given $0 < α < 1$ , the Beatty sequence of density $α$ is the sequence $B_{α} = (⌊ n / α ⌋)_{n \in N}$ . Beatty's theorem states that if $α, β$ are irrational numbers with $α+…

math.NT2018★ 1 cited

A binary quadratic Titchmarsh divisor problem

Junxian Li

We consider a binary quadratic variant of the Titchmarsh divisor problem and give an asymptotic formula for $\sum_{p^{2} + q^{2} \leq N} τ (p^{2} + q^{2} + 1)$ , where $p, q$ are primes.

math.NT2017

Leading Digits of Mersenne Numbers

Zhaodong Cai, Matthew Faust, A. J. Hildebrand +2

It has long been known that sequences such as the powers of $2$ and the factorials satisfy Benford's Law; that is, leading digits in these sequences occur with frequencies given by…

math.NT2017★ 6 cited

On distinct consecutive $r$ -differences

Junxian Li, George Shakan

Suppose $A \subset R$ of size $k$ has distinct consecutive $r$ --differences, that is for $1 \leq i \leq k - r$ , the $r$ --tuples $$(a_{i+1} - a_i , \ldots , a_{i+r} - a_{i +…

math.NT2016

A lower bound for the least prime in an arithmetic progression

Junxian Li, Kyle Pratt, George Shakan

Fix $k$ a positive integer, and let $ℓ$ be coprime to $k$ . Let $p (k, ℓ)$ denote the smallest prime equivalent to $ℓ (mod k)$ , and set $P (k)$ to be the maximum of all the $…