On the convergence rate of the partial sums of positive entire Dirichlet series

1991 ◽  
Vol 17 (1) ◽  
pp. 47-54 ◽  
Author(s):  
M. H. Шеремета
Keyword(s):  
Convergence Rate ◽  
Dirichlet Series ◽  
Partial Sums ◽  
Entire Dirichlet Series

scholarly journals Variant of the truncated Perron formula and primes in polynomial sets

2019 ◽  
Vol 16 (02) ◽  
pp. 309-323
Author(s):  
D. S. Ramana ◽  
O. Ramaré
Keyword(s):  
Dirichlet Series ◽  
Riemann Hypothesis ◽  
Partial Sums ◽  
Generalized Riemann Hypothesis ◽  
Perron’S Formula ◽  
Polynomial Formula

We show under the Generalized Riemann Hypothesis that for every non-constant integer-valued polynomial [Formula: see text], for every [Formula: see text], and almost every prime [Formula: see text] in [Formula: see text], the number of primes from the interval [Formula: see text] that are values of [Formula: see text] modulo [Formula: see text] is the expected one, provided [Formula: see text] is not more than [Formula: see text]. We obtain this via a variant of the classical truncated Perron’s formula for the partial sums of the coefficients of a Dirichlet series.

A Multiplicative Analogue of Schur's Tauberian Theorem

2003 ◽  
Vol 46 (3) ◽  
pp. 473-480 ◽  
Author(s):  
Karen Yeats
Keyword(s):  
Power Series ◽  
Asymptotic Behaviour ◽  
Dirichlet Series ◽  
Tauberian Theorem ◽  
Partial Sums ◽  
Regularly Varying Functions ◽  
Regularly Varying

AbstractA theorem concerning the asymptotic behaviour of partial sums of the coefficients of products of Dirichlet series is proved using properties of regularly varying functions. This theorem is a multiplicative analogue of Schur's Tauberian theorem for power series.

Paley Effect for Entire Dirichlet Series

2015 ◽  
Vol 67 (6) ◽  
pp. 838-852
Author(s):  
T. Ya. Hlova ◽  
P. V. Filevych
Keyword(s):  
Dirichlet Series ◽  
Entire Dirichlet Series

scholarly journals Character sums and the series L(1, χ)

2001 ◽  
Vol 70 (3) ◽  
pp. 425-436
Author(s):  
Ming-Guang Leu
Keyword(s):  
Dirichlet Series ◽  
Character Sums ◽  
Partial Sums

AbstractIn this paper we derive a relation between character sums and partial sums of Dirichlet series.

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