منابع مشابه
Natural Boundaries of Dirichlet Series
We prove some conditions on the existence of natural boundaries of Dirichlet series. We show that generically the presumed boundary is the natural one. We also give an application of natural boundaries in determining asymptotic results.
متن کاملNatural Boundary of Random Dirichlet Series
For the random Dirichlet series ∞ ∑ n=0 Xn(ω) e−sλn (s = σ + it ∈ C, 0 = λ0 < λn ↑ ∞), whose coefficients are uniformly nondegenerate independent random variables, we provide some explicit conditions for the line of convergence to be its natural boundary a.s. Running Title Natural Boundary of Random Dirichlet Series
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 کاملDirichlet Series
where the an are complex numbers and s is a complex variable. Such functions are called Dirichlet series. We call a1 the constant term. A Dirichlet series will often be written as ∑ ann −s, with the index of summation understood to start at n = 1. Similarly, ∑ app −s runs over the primes, and ∑ apkp −ks runs over the prime powers excluding 1. (Not counting 1 as a prime power in that notation is...
متن کاملOn Kubota’s Dirichlet Series
Kubota [19] showed how the theory of Eisenstein series on the higher metaplectic covers of SL2 (which he discovered) can be used to study the analytic properties of Dirichlet series formed with n-th order Gauss sums. In this paper we will prove a functional equation for such Dirichlet series in the precise form required by the companion paper [2]. Closely related results are in Eckhardt and Pat...
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ژورنال
عنوان ژورنال: Functiones et Approximatio Commentarii Mathematici
سال: 2007
ISSN: 0208-6573
DOI: 10.7169/facm/1229618738