THIRTY-TWO GOLDBACH VARIATIONS-Reference-Cited by-同舟云学术

THIRTY-TWO GOLDBACH VARIATIONS

Published:2006-03 Issue:01 Volume:02 Page:65-103
ISSN:1793-0421
Container-title:International Journal of Number Theory
language:en
Short-container-title:Int. J. Number Theory

Author:

BORWEIN JONATHAN M.¹,BRADLEY DAVID M.²

Affiliation:

1. Faculty of Computer Science, Dalhousie University, Halifax, Nova Scotia B3H 1W5, Canada

2. Department of Mathematics & Statistics, University of Maine, 5752 Neville Hall Orono, Maine 04469-5752, USA

Abstract

We give thirty-two diverse proofs of a small mathematical gem — the fundamental Euler sum identity [Formula: see text] We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby illustrating both the wide variety of techniques fruitfully used to study such sums and the attraction of their study.

Publisher

World Scientific Pub Co Pte Lt

Subject

Algebra and Number Theory

Link

https://www.worldscientific.com/doi/pdf/10.1142/S1793042106000383

Reference71 articles.

1. Borwein and Bradley's Apérv-Like Formulae for ζ(4n + 3)

2. Ramanujan’s Notebooks

Cited by 40 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On a result of Koecher concerning Markov–Apéry-type formulas for the Riemann zeta function;International Journal of Number Theory;2022-09-05

2. Multivariable connected sums and multiple polylogarithms;Research in the Mathematical Sciences;2021-12-17

3. In The Shadow of Euler’s Greatness: Adventures in the Rediscovery of an Intriguing Sum;The Mathematical Intelligencer;2021-07-29

4. Structural properties of multiple zeta values;International Journal of Number Theory;2021-04-20

5. Explicit Evaluation of Some Quadratic Euler-Type Sums Containing Double-Index Harmonic Numbers;Tatra Mountains Mathematical Publications;2020-12-01