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Start Over Subject Dirichlet series

1. A study of various results for a class of entire Dirichlet series with complex frequencies

Creator:
Kumar, Niraj and Manocha, Garima
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Dirichlet series, Banach algebra, topological zero divisor, division algebra, continuous linear functional, and total set
Language:
English
Description:
Let F be a class of entire functions represented by Dirichlet series with complex frequencies ∑ ake hλ k ,zi for which (|λ k |/e)|λ k | k!|ak| is bounded. Then F is proved to be a commutative Banach algebra with identity and it fails to become a division algebra. F is also proved to be a total set. Conditions for the existence of inverse, topological zero divisor and continuous linear functional for any element belonging to F have also been established.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. The growth of Dirichlet series

Creator:
Gu, Zhendong and Sun, Daochun
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Dirichlet series, order, and abscissa of convergence
Language:
English
Description:
We define Knopp-Kojima maximum modulus and the Knopp-Kojima maximum term of Dirichlet series on the right half plane by the method of Knopp-Kojima, and discuss the relation between them. Then we discuss the relation between the Knopp-Kojima coefficients of Dirichlet series and its Knopp-Kojima order defined by Knopp-Kojima maximum modulus. Finally, using the above results, we obtain a relation between the coefficients of the Dirichlet series and its Ritt order. This improves one of Yu Jia-Rong's results, published in Acta Mathematica Sinica 21 (1978), 97–118. We also give two examples to show that the condition under which the main result holds can not be weakened.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public