Rook theory, compositions, and zeta functions-Reference-Cited by-同舟云学术

Rook theory, compositions, and zeta functions

Published:1996 Issue:9 Volume:348 Page:3799-3825
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Haglund James

Abstract

A new family of Dirichlet series having interesting combinatorial properties is introduced. Although they have no functional equation or Euler product, under the Riemann Hypothesis it is shown that these functions have no zeros in R e ( s ) > 1 / 2 \mathrm {Re}(s)>1/2 . Some identities in the ring of formal power series involving rook theory and continued fractions are developed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1996-348-09/S0002-9947-96-01662-5/S0002-9947-96-01662-5.pdf

Reference26 articles.

1. Some new observations on the Göllnitz-Gordon and Rogers-Ramanujan identities;Alladi, Krishnaswami;Trans. Amer. Math. Soc.,1995

2. Encyclopedia of Mathematics and its Applications, Vol. 2;Andrews, George E.,1976

3. The theory of compositions. I. The ordered factorizations of 𝑛 and a conjecture of C. Long;Andrews, George E.;Canad. Math. Bull.,1975

4. The theory of compositions. II. Simon Newcomb’s problem;Andrews, George E.;Utilitas Math.,1975

5. The theory of compositions. II. Simon Newcomb’s problem;Andrews, George E.;Utilitas Math.,1975

Cited by 2 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. Theorems and Conjectures Involving Rook Polynomials with Only Real Zeros;Topics in Number Theory;1999

2. The Combinatorics behind Number-Theoretic Sieves;Advances in Mathematics;1998-09