A note on abscissas of Dirichlet series
نویسندگان
چکیده
منابع مشابه
Bohr and Rogosinski Abscissas for Ordinary Dirichlet Series
We prove that the abscissas of Bohr and Rogosinski for ordinary Dirichlet series, mapping the right half-plane into the bounded convex domain G ⊂ C are independent of the domain G. Furthermore, we obtain new estimates about these abscissas. 1. Preliminaries Let us recall the theorem of H.Bohr [19] in 1914. Theorem 1.1. If a power series
متن کاملNote on Absolutely Convergent Dirichlet Series
is it true that \f(s)\ s^k>0 for cr^O implies that (/(s))-1 is also of the form (1)? In this note, an affirmative answer is supplied.3 Let P be the semigroup of positive integers under multiplication, and let h(P) be the class of all complex functions a on P, a= {an}»~i, for which ||a|| = y^°-i \an\ is finite. We obtain a commutative Banach algebra by defining (aa)n = aan for complex a, (a+b)n ...
متن کاملA Note on Dirichlet Characters
Denoting by r(k, m, p) the first occurrence of m consecutive fcth power residues of a prime p = 1 (mod k), we show that r(k, m, p) > c log p for infinitely many p (c is an absolute constant) provided that k is even and m ä 3.
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...
متن کاملA note on lacunary series in $mathcal{Q}_K$ spaces
In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.
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: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
سال: 2019
ISSN: 1578-7303,1579-1505
DOI: 10.1007/s13398-019-00647-y