Lilu Zhao

activity

20082026

most citedSums of four squares of primes

6 citations · 19 across the 20 of their papers we have counts for

collaborators

Showing 2014Show all

4 papers · 1 filter

math.NT2014★ 1 cited

The quadratic form in 9 prime variables

Lilu Zhao

Let $f (x_{1}, \dots, x_{n})$ be a regular indefinite integral quadratic form with $n \geq 9$ , and let $t$ be an integer. It is established that $f (x_{1}, \dots, x_{n}) = t$ has solutions in prim…

math.NT2014

On restricted sumsets over a field

Lilu Zhao

We consider restricted sumsets over field $F$ . Let\begin{align*}C=\{a_1+\cdots+a_n:a_1\in A_1,\ldots,a_n\in A_n, a_i-a_j\notin S_{ij}\ \text{if}\ i\not=j\},\end{align*} where $S_{i…

math.NT2014

Exceptional sets in Waring's problem: two squares and s biquadrates

Lilu Zhao

Let $R_{s} (n)$ denote the number of representations of the positive number $n$ as the sum of two squares and $s$ biquadrates. When $s = 3$ or $4$ , it is established that the anticipate…

math.NT2014

The sum of divisors of a quadratic form

Lilu Zhao

We study the sum of divisors of the quadratic form $m_{1}^{2} + m_{2}^{2} + m_{3}^{2}$ . Let $S_{3} (X) = 1 \leq m_{1}, m_{2}, m_{3} \leq X \sum τ (m_{1}^{2} + m_{2}^{2} + m_{3}^{2}) .$ We obtain the asymptotic formula $$S_3(X)=C…