Rational series for multiple zeta and log gamma functions
نویسندگان
چکیده
منابع مشابه
Rational series for multiple zeta and log gamma functions
We give series expansions for the Barnes multiple zeta functions in terms of rational functions whose numerators are complex-order Bernoulli polynomials, and whose denominators are linear. We also derive corresponding rational expansions for Dirichlet L-functions and multiple log gamma functions in terms of higher order Bernoulli polynomials. These expansions naturally express many of the well-...
متن کاملOn p-adic multiple zeta and log gamma functions
We define p-adic multiple zeta and log gamma functions using multiple Volkenborn integrals, and develop some of their properties. Although our functions are close analogues of classical Barnes multiple zeta and log gamma functions and have many properties similar to them, we find that our p-adic analogues also satisfy reflection functional equations which have no analogues to the complex case. ...
متن کاملOn Eulerian Log-Gamma Integrals and Tornheim–Witten Zeta Functions
Stimulated by earlier work by Moll and his coworkers [1], we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim– Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate
متن کاملThe Multiple Gamma-Functions and the Log-Gamma Integrals
In this paper, which is a companion paper to W , starting from the Euler integral which appears in a generalization of Jensen’s formula, we shall give a closed form for the integral of log Γ 1± t . This enables us to locate the genesis of two new functions A1/a and C1/a considered by Srivastava and Choi. We consider the closely related function A(a) and the Hurwitz zeta function, which render t...
متن کاملMultiple Dirichlet Series and Moments of Zeta and L–functions
This paper develops an analytic theory of Dirichlet series in several complex variables which possess sufficiently many functional equations. In the first two sections it is shown how straightforward conjectures about the meromorphic continuation and polar divisors of certain such series imply, as a consequence, precise asymptotics (previously conjectured via random matrix theory) for moments o...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2013
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2013.05.016