Joint value-distribution theorems on Lerch zeta-functions. II
نویسندگان
چکیده
منابع مشابه
Joint Value-distribution Theorems on Lerch Zeta-functions. Ii
We give corrected statements of some theorems from [5] and [6] on joint value distribution of Lerch zeta-functions (limit theorems, universality, functional independence). We also present a new direct proof of a joint limit theorem in the space of analytic functions and an extension of a joint universality theorem.
متن کاملGeometric Studies on Inequalities of Harmonic Functions in a Complex Field Based on ξ-Generalized Hurwitz-Lerch Zeta Function
Authors, define and establish a new subclass of harmonic regular schlicht functions (HSF) in the open unit disc through the use of the extended generalized Noor-type integral operator associated with the ξ-generalized Hurwitz-Lerch Zeta function (GHLZF). Furthermore, some geometric properties of this subclass are also studied.
متن کاملTwo-Variable Zeta-Functions on Graphs and Riemann–Roch Theorems
We investigate, in this article, a generalization of the Riemann–Roch theorem for graphs of Baker and Norine, with a view toward identifying new objects for which a two-variable zeta-function can be defined. To a lattice Λ of rank n − 1 in Z n and perpendicular to a positive integer vector R, we define the notions of g-number and of canonical vector , in analogy with the notions of genus and ca...
متن کاملThe Lerch zeta function IV. Hecke operators
This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators {Tm : m ≥ 1} given by Tm(f )(a, c) = 1 m ∑m−1 k=0 f ( a+k m ,mc) acting on certain spaces of real-analytic functions, including Lerch zeta functions for various parameter values. The actions of various related operators on these function spaces are de...
متن کاملSome Mean Value Theorems for the Riemann Zeta-function and Dirichlet L-functions
The theory of the Riemann zeta-function ζ(s) and Dirichlet L-functions L(s, χ) abounds with unsolved problems. Chronologically the first of these, now known as the Riemann Hypothesis (RH), originated from Riemann’s remark that it is very probable that all non-trivial zeros of ζ(s) lie on the line < s = 12 . Later on Piltz conjectured the same for all of the functions L(s, χ) (GRH). The vertical...
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: Lithuanian Mathematical Journal
سال: 2006
ISSN: 0363-1672,1573-8825
DOI: 10.1007/s10986-006-0027-x