Zhi-Wei Sun

activity

20032026

most citedSuper congruences and Euler numbers

127 citations · 565 across the 184 of their papers we have counts for

collaborators

Showing 2011Show all

7 papers · 1 filter

math.NT2011★ 2 cited

Congruences for Franel numbers

Zhi-Wei Sun

The Franel numbers given by $f_{n} = \sum_{k = 0}^{n} (k n)^{3}$ ( $n = 0, 1, 2, \dots$ ) play important roles in both combinatorics and number theory. In this paper we initiate the systemat…

math.NT2011

p-adic congruences motivated by series

Zhi-Wei Sun

Let $p > 5$ be a prime. Motivated by the known formulae $\sum_{k = 1}^{\infty} (- 1)^{k} / (k^{3} (k 2 k)) = - 2 ζ (3) /5$ and $\sum_{k = 0}^{\infty} (k 2 k)^{2} / ((2 k + 1) 1 6^{k}) = 4 G / π$ $(w h er e$ G=\su…

math.NT2011★ 7 cited

Some new series for $1/ π$ and related congruences

Zhi-Wei Sun

In this paper we prove some new series for $1/ π$ as well as related congruences. We also raise several new kinds of series for $1/ π$ and present some related conjectural congruence…

math.NT2011★ 8 cited

Conjectures and results on $x^{2}$ mod $p^{2}$ with $4 p = x^{2} + d y^{2}$

Zhi-Wei Sun

Given a squarefree positive integer $d$ , we want to find integers (or rational numbers with denominators not divisible by large primes) $a_{0}, a_{1}, a_{2}, \dots$ such that for sufficien…

math.CA2011

List of conjectural series for powers of $π$ and other constants

Zhi-Wei Sun

The author gives the full list of his conjectures on series for powers of $π$ and other important constants scattered in some of his public papers or his private diaries. The list…

math.NT2011★ 8 cited

On sums of Apéry polynomials and related congruences

Zhi-Wei Sun

The Apéry polynomials are given by $A_{n} (x) = k = 0 \sum n (k n)^{2} (k n + k)^{2} x^{k} (n = 0, 1, 2, \dots) .$ (Those $A_{n} = A_{n} (1)$ are Apéry numbers.) Let $p$ be an odd prime. We show…

Congruences for Franel numbers

p-adic congruences motivated by series

Some new series for 1/π and related congruences

Conjectures and results on x2 mod p2 with 4p=x2+dy2

List of conjectural series for powers of π and other constants

On sums of Apéry polynomials and related congruences

Some new series for $1/ π$ and related congruences

Conjectures and results on $x^{2}$ mod $p^{2}$ with $4 p = x^{2} + d y^{2}$

List of conjectural series for powers of $π$ and other constants