On the Dirichlet series related to the cubic theta function

Author： Proskurin N.  

Publisher： Springer Publishing Company

ISSN： 1072-3374

Source： Journal of Mathematical Sciences, Vol.143, Iss.3, 2007-06, pp. : 3137-3148

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Abstract

The paper studies the function L(τ;·) defined by the Dirichlet series , where τ(&ugr;) is the &ugr;th Fourier coefficient of the Kubota-Patterson cubic theta function. For this function, an exact and an approximate functional equations are derived. It is established that the function does not vanish in the halfplane Re s ≥ 1.3533 and has no singularities except for a simple pole at the point 5/6. Issues related to computing the coefficients τ(υ) and values of the special functions arising in the approximate functional equation are considered. Bibliography: 11 titles.

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