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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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
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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 $\mathrm {Re}(s)>1/2$. Some identities in the ring of formal power series involving rook theory and continued fractions are developed.

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

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