The Hoheisel phenomenon for generalized Dirichlet series
نویسندگان
چکیده
منابع مشابه
Generalized multiple Dirichlet series and generalized multiple polylogarithms
where t is a complex variable. By Assumption I, we see that the series (1.3) is convergent when <t < 0. We further assume the following: (Assumption II ) ψ(s) can be continued analytically to the whole complex plane C, and holomorphic for all s ∈ C. In any fixed strip σ1 ≤ σ ≤ σ2, ψ(s; u) is uniformly convergent to ψ(s) as u → 1 + 0. Furthermore there exists a certain θ0 = θ0(σ1, σ2) ∈ R with 0...
متن کاملGeneralized Ritt type and generalized Ritt weak type connected growth properties of entire functions represented by vector valued Dirichlet series
In this paper, we introduce the idea of generalized Ritt type and generalised Ritt weak type of entire functions represented by a vector valued Dirichlet series. Hence, we study some growth properties of two entire functions represented by a vector valued Dirichlet series on the basis of generalized Ritt type and generalised Ritt weak type.
متن کاملOn Some Results in the Light of Generalized Relative Ritt Order of Entire Functions Represented by Vector Valued Dirichlet Series
In this paper, we study some growth properties of entire functions represented by a vector valued Dirichlet series on the basis of generalized relative Ritt order and generalized relative Ritt lower order.
متن کاملAnalytical D’Alembert Series Solution for Multi-Layered One-Dimensional Elastic Wave Propagation with the Use of General Dirichlet Series
A general initial-boundary value problem of one-dimensional transient wave propagation in a multi-layered elastic medium due to arbitrary boundary or interface excitations (either prescribed tractions or displacements) is considered. Laplace transformation technique is utilised and the Laplace transform inversion is facilitated via an unconventional method, where the expansion of complex-valued...
متن کاملDirichlet Series
This definition could have been given to an 18th or early 19th century mathematical audience, but it would not have been very popular: probably they would not have been comfortable with the Humpty Dumpty-esque redefinition of multiplication. Mathematics at that time did have commutative rings: rings of numbers, of matrices, of functions, but not rings with a “funny” multiplication operation def...
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: Proceedings of the American Mathematical Society
سال: 1973
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1973-0327682-0