An infinite family of zeta functions indexed by Hermite polynomials

DOI10.1016/0022-247X(89)90102-9zbMath0674.10035MaRDI QIDQ1121317

S. F. Keating

Publication date: 1989

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

functional equationRiemann hypothesisanalytic continuationgeneralized zeta functionsgeneralized Jacobi inversion formula

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Other Dirichlet series and zeta functions (11M41)

Related Items (10)

Mellin transforms of a generalization of Legendre polynomials ⋮ An infinite family of summation identities ⋮ ON THE RIEMANN HYPOTHESIS, AREA QUANTIZATION, DIRAC OPERATORS, MODULARITY, AND RENORMALIZATION GROUP ⋮ An infinite family of zeta functions indexed by Hermite polynomials ⋮ Theta and Riemann xi function representations from harmonic oscillator eigensolutions ⋮ ON STRATEGIES TOWARDS THE RIEMANN HYPOTHESIS: FRACTAL SUPERSYMMETRIC QM AND A TRACE FORMULA ⋮ THE RIEMANN HYPOTHESIS IS A CONSEQUENCE OF $\mathcal{CT}$-INVARIANT QUANTUM MECHANICS ⋮ On the Riemann hypothesis, complex scalings and logarithmic time reversal ⋮ Special functions and the Mellin transforms of Laguerre and Hermite functions ⋮ Zeros of symmetric, quasi-definite, orthogonal polynomials

Cites Work

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