Mean Values of Zeta - Functions via Representation Theory
نویسندگان
چکیده
We shall see that in these cases the spectra come from irreducible representations of G occurring in L2(Γ\G), and that the resulting integral transform of g has a kernel composed of Bessel functions of representations of G. It should be noted that (2) can readily be extended to any imaginary quadratic number field of class number one. Other examples that share the same structure and have been more or less worked out are
منابع مشابه
Spectral zeta functions of graphs and the Riemann zeta function in the critical strip
We initiate the study of spectral zeta functions ⇣X for finite and infinite graphs X, instead of the Ihara zeta function, with a perspective towards zeta functions from number theory and connections to hypergeometric functions. The Riemann hypothesis is shown to be equivalent to an approximate functional equation of graph zeta functions. The latter holds at all points where Riemann’s zeta funct...
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 کاملRecent Developments in the Mean Square Theory of the Riemann Zeta and Other Zeta-Functions
The purpose of the present article is to survey some mean value results obtained recently in zeta-function theory. We do not mention other important aspects of the theory of zeta-functions, such as the distribution of zeros, value-distribution, and applications to number theory. Some of them are probably treated in the articles of Professor Apostol and Professor Ramachandra in the present volum...
متن کاملOn Validated Numeric of Values of Some Zeta and L-functions, and Applications
This note is for an introduction to the validated numerics study of values of zeta and L functions. The subject matter of this talk lies in the area between Analysis, Algebra and Validated Numerics [1, 7].More specifically, I want to discuss the relations between the algebra and analysis of zeta and L functions and the evaluation of values of the functions. The talk is on some observations and ...
متن کاملSome Convexity Properties of Dirichlet Series with Positive Terms
Some basic results for Dirichlet series ψ with positive terms via log-convexity properties are pointed out. Applications for Zeta, Lambda and Eta functions are considered. The concavity of the function 1/ψ is explored and, as a main result, it is proved that the function 1/ζ is concave on (1,∞) . As a consequence of this fundamental result it is noted that Zeta at the odd positive integers is b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2006