Three new representations are derived for the Dirichlet series of Wigert's divisor function d^(1/k)(j) for k >= 2, one analogous to the Chowla-Selberg formula, along with meromorphicity and an expression for F_3(3/2) involving Bessel functions.
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Derives formulas for Koshliakov zeta functions at integer values, recovers Euler-Ramanujan zeta results in the p to infinity limit, and introduces p-analogues of Eisenstein series transformations and Ramanujan polynomials with functional equations.
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A divisor function of Wigert and higher degree forms
Three new representations are derived for the Dirichlet series of Wigert's divisor function d^(1/k)(j) for k >= 2, one analogous to the Chowla-Selberg formula, along with meromorphicity and an expression for F_3(3/2) involving Bessel functions.
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On special values of Koshliakov zeta functions
Derives formulas for Koshliakov zeta functions at integer values, recovers Euler-Ramanujan zeta results in the p to infinity limit, and introduces p-analogues of Eisenstein series transformations and Ramanujan polynomials with functional equations.