Yu-Chen Sun

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20172019

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math.NT2018

A note on the sum of reciprocals

Yuchen Ding, Yu-Chen Sun

For a fixed positive integer $m$ and any partition $m = m_{1} + m_{2} + \dots + m_{e}$ , there exists a sequence ${n_{i}}_{i = 1}^{k}$ of positive integers such that $$m=\frac{1}{n_{1}}…

math.NT2018

On the gaps between consecutive primes

Yu-Chen Sun, Hao Pan

Let $p_{n}$ denote the $n$ -th prime. For any $m \geq 1$ , there exist infinitely many $n$ such that $p_{n} - p_{n - m} \leq C_{m}$ for some large constant $C_{m} > 0$ , and $$p_{n+1}-p_n\geq \frac…

math.NT2017

The Green-Tao theorem for primes of the form $x^{2} + y^{2} + 1$

Yu-Chen Sun, Hao Pan

We prove that the primes of the form $x^{2} + y^{2} + 1$ contain arbitrarily long non-trivial arithmetic progressions.

A note on the sum of reciprocals

On the gaps between consecutive primes

The Green-Tao theorem for primes of the form x2+y2+1

The Green-Tao theorem for primes of the form $x^{2} + y^{2} + 1$