scholarly journals Dirichlet twists of GL n -automorphic L-functions and hyper-Kloosterman Dirichlet series

2021 ◽  
Vol 30 (3) ◽  
pp. 633-703
Author(s):  
Jeanine Van Order
Keyword(s):  
Dirichlet Series

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 The General Theory of Dirichlet Series

Nature ◽  
1915 ◽  
Vol 96 (2403) ◽  
pp. 312-312
Author(s):  
G. B. M.
Keyword(s):  
General Theory ◽  
Dirichlet Series

scholarly journals One-Sided Tauberian Theorems for Dirichlet Series Methods of Summability

2001 ◽  
Vol 31 (3) ◽  
pp. 797-830 ◽  
Author(s):  
David Borwein ◽  
Werner Kratz ◽  
Ulrich Stadtmüller
Keyword(s):  
Dirichlet Series ◽  
Tauberian Theorems

scholarly journals On the zeros of a class of generalised Dirichlet series-VI

1981 ◽  
Vol 19 (1-2) ◽  
pp. 239-250 ◽  
Author(s):  
R. Balasubramanian ◽  
K. Ramachandra
Keyword(s):  
Dirichlet Series

scholarly journals On Dirichlet series attached to cusp forms and the Siegel-zero

1984 ◽  
Vol 25 (1) ◽  
pp. 107-119 ◽  
Author(s):  
F. Grupp
Keyword(s):  
Dirichlet Series ◽  
Cusp Form ◽  
Fourier Expansion ◽  
Dirichlet Character ◽  
Hecke Operators ◽  
Cusp Forms ◽  
Siegel Zero ◽  
Image Position

Let k be an even integer greater than or equal to 12 and f an nonzero cusp form of weight k on SL(2, Z). We assume, further, that f is an eigenfunction for all Hecke-Operators and has the Fourier expansionFor every Dirichlet character xmod Q we define

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