Rook theory, compositions, and zeta functions

Author:
James Haglund

Journal:
Trans. Amer. Math. Soc. **348** (1996), 3799-3825

MSC (1991):
Primary 11M41, 05A15

MathSciNet review:
1357880

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 . Some identities in the ring of formal power series involving rook theory and continued fractions are developed.

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Additional Information

**James Haglund**

Affiliation:
Department of Mathematics, The University of Illinois at Urbana-Champaign, Urbana, IL 61801

Email:
jhaglund@math.uiuc.edu

DOI:
http://dx.doi.org/10.1090/S0002-9947-96-01662-5

Keywords:
Riemann zeta function,
Riemann hypothesis,
continued fraction,
composition,
rook theory,
Euler product

Received by editor(s):
January 20, 1995

Received by editor(s) in revised form:
November 6, 1995

Article copyright:
© Copyright 1996
American Mathematical Society