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Rook theory, compositions, and zeta functions

Author(s): James Haglund
Journal: Trans. Amer. Math. Soc. 348 (1996), 3799-3825.
MSC (1991): Primary 11M41, 05A15
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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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Additional Information:

James Haglund
Affiliation: Department of Mathematics, The University of Illinois at Urbana-Champaign, Urbana, IL 61801
Email: jhaglund@math.uiuc.edu

DOI: 10.1090/S0002-9947-96-01662-5
PII: S 0002-9947(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
Copyright of article: Copyright 1996, American Mathematical Society

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