scholarly journals Boundary behaviour of Dirichlet series with applications to universal series

2016 ◽  
Vol 48 (5) ◽  
pp. 735-744 ◽  
Author(s):  
Stephen J. Gardiner ◽  
Myrto Manolaki
Keyword(s):  
Dirichlet Series ◽  
Boundary Behaviour ◽  
Universal Series

Abstract theory of universal series and an application to Dirichlet series

2005 ◽  
Vol 341 (9) ◽  
pp. 539-543 ◽  
Author(s):  
Vassili Nestoridis ◽  
Chris Papadimitropoulos
Keyword(s):  
Dirichlet Series ◽  
Universal Series ◽  
Abstract Theory

Cancellation in algebraic twisted sums on GL_ m

2021 ◽  
Vol 33 (4) ◽  
pp. 1061-1082
Author(s):  
Yujiao Jiang ◽  
Guangshi Lü
Keyword(s):  
Dirichlet Series ◽  
Central Character ◽  
Multiplicative Functions ◽  
Cuspidal Representation ◽  
Series Coefficient

Abstract Let π be an automorphic irreducible cuspidal representation of GL m {\operatorname{GL}_{m}} over ℚ {\mathbb{Q}} with unitary central character, and let λ π ⁢ ( n ) {\lambda_{\pi}(n)} be its n-th Dirichlet series coefficient. We study short sums of isotypic trace functions associated to some sheaves modulo primes q of bounded conductor, twisted by multiplicative functions λ π ⁢ ( n ) {\lambda_{\pi}(n)} and μ ⁢ ( n ) ⁢ λ π ⁢ ( n ) {\mu(n)\lambda_{\pi}(n)} . We are able to establish non-trivial bounds for these algebraic twisted sums with intervals of length of at least q 1 / 2 + ε {q^{1/2+\varepsilon}} for an arbitrary fixed ε > 0 {\varepsilon>0} .

scholarly journals A dominated convergence theorem for Eisenstein series

2021 ◽  
Author(s):  
Johann Franke
Keyword(s):  
Fourier Series ◽  
Dirichlet Series ◽  
Eisenstein Series ◽  
Modular Forms ◽  
Convergence Theorem ◽  
Rational Functions ◽  
New Approach ◽  
Series Representations ◽  
Dominated Convergence ◽  
Generalized Dirichlet

AbstractBased on the new approach to modular forms presented in [6] that uses rational functions, we prove a dominated convergence theorem for certain modular forms in the Eisenstein space. It states that certain rearrangements of the Fourier series will converge very fast near the cusp $$\tau = 0$$ τ = 0 . As an application, we consider L-functions associated to products of Eisenstein series and present natural generalized Dirichlet series representations that converge in an expanded half plane.

scholarly journals Function-Theoretic Metrics and Boundary Behaviour of Functions Meromorphic or Holomorphic in the Unit Disk

1972 ◽  
Vol 45 ◽  
pp. 109-117
Author(s):  
Shinji Yamashita
Keyword(s):  
Unit Disk ◽  
Boundary Behaviour ◽  
Arc Length

The metrics to which the title of the present paper refers are expressed in the form of elements of arc length as follows:

Sign in / Sign up

Export Citation Format

Share Document