Rook theory, compositions, and zeta functions

Haglund, James

doi:10.1090/S0002-9947-96-01662-5

Rook theory, compositions, and zeta functions
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by James Haglund

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

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

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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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