On a secant Dirichlet series and Eichler integrals of Eisenstein series
نویسندگان
چکیده
منابع مشابه
On a Secant Dirichlet Series and Eichler Integrals of Eisenstein Series
We consider, for even s, the secant Dirichlet series ψs(τ) = ∑∞ n=1 sec(πnτ) ns , recently introduced and studied by Laĺın, Rodrigue and Rogers. In particular, we show, as conjectured and partially proven by Laĺın, Rodrigue and Rogers, that the values ψ2m( √ r), with r > 0 rational, are rational multiples of π2m. We then put the properties of the secant Dirichlet series into context by showing ...
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In his lost notebook, Ramanujan recorded a formula relating a “character analogue” of the Dedekind eta-function, the integral of a quotient of eta-functions, and the value of a Dirichlet Lfunction at s = 2. Here we derive an infinite family of formulas which includes Ramanujan’s original formula as a special case. Our results depend on a representation of values of the derivatives of Dirichlet ...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2016
ISSN: 0025-5874,1432-1823
DOI: 10.1007/s00209-016-1675-0