multiplier system
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2014 ◽  
Vol 57 (3) ◽  
pp. 317-319
Author(s):  
Z. K. Nurubeyli ◽  
K. Z. Nuriyev ◽  
K. B. Gurbanov ◽  
Sh. Sh. Alekberov ◽  
G. M. Kerimov ◽  
...  


2012 ◽  
Vol 54 (2) ◽  
pp. 355-358
Author(s):  
YOUNGJU CHOIE ◽  
WINFRIED KOHNEN

AbstractLet f be a non-zero cusp form with real Fourier coefficients a(n) (n ≥ 1) of positive real weight k and a unitary multiplier system v on a subgroup Γ ⊂ SL2(ℝ) that is finitely generated and of Fuchsian type of the first kind. Then, it is known that the sequence (a(n))(n ≥ 1) has infinitely many sign changes. In this short note, we generalise the above result to the case of entire modular integrals of non-positive integral weight k on the group Γ0*(N) (N ∈ ℕ) generated by the Hecke congruence subgroup Γ0(N) and the Fricke involution $W_N:= \big(\scriptsize\begin{array}{c@{}c} 0 & -{1/\sqrt N} \\[3pt] \sqrt N & 0\\ \end{array}\big)$ provided that the associated period functions are polynomials.



2012 ◽  
Vol 39 (1) ◽  
pp. 18-25 ◽  
Author(s):  
Fatemeh S. Rasouli ◽  
S. Farhad Masoudi ◽  
Yaser Kasesaz


2007 ◽  
Vol 03 (03) ◽  
pp. 335-347 ◽  
Author(s):  
WLADIMIR DE AZEVEDO PRIBITKIN

We introduce a class of functions that generalize the epoch-making series of Poincaré and Petersson. Our "uninhibited Poincaré series" permits both a complex weight and an arbitrary multiplier system that is independent of the weight. In this initial paper we provide their Fourier expansions, as well as their modular behavior. We show that they are modular integrals that possess interesting periods. Moreover, we establish with relative ease that they "almost never" vanish identically. Along the way we present a seemingly unknown historical truth concerning Kloosterman sums, and also an alternative approach to Petersson's factor systems. The latter depends upon a simple multiplication rule.



1999 ◽  
Vol 69 (229) ◽  
pp. 65-83 ◽  
Author(s):  
Einar Haug ◽  
Ragnar Winther


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