scholarly journals A Hecke correspondence theorem for automorphic integrals with symmetric rational period functions on the Hecke groups

2010 ◽  
Vol 130 (12) ◽  
pp. 2732-2744 ◽  
Author(s):  
Wendell Ressler
Keyword(s):  
Hecke Groups ◽  
Hecke Correspondence ◽  
Rational Period Functions ◽  
Correspondence Theorem ◽  
Automorphic Integrals

A Hecke correspondence theorem for automorphic integrals with infinite log-polynomial sum period functions

2014 ◽  
Vol 10 (07) ◽  
pp. 1857-1879 ◽  
Author(s):  
Austin Daughton
Keyword(s):  
Functional Equation ◽  
Dirichlet Series ◽  
Vertical Strip ◽  
Hecke Groups ◽  
Hecke Correspondence ◽  
Correspondence Theorem ◽  
Automorphic Integrals

We generalize the correspondence between Dirichlet series with finitely many poles that satisfy a functional equation and automorphic integrals with log-polynomial sum period functions. In particular, we extend the correspondence to hold for Dirichlet series with finitely many essential singularities. We also study Dirichlet series with infinitely many poles in a vertical strip. For Hecke groups with λ ≥ 2 and some weights, we prove a similar correspondence for these Dirichlet series. For this case, we provide a way to estimate automorphic integrals with infinite log-polynomial periods by automorphic integrals with finite log-polynomial periods.

scholarly journals Parity patterns associated with lifts of Hecke groups

2008 ◽  
Vol 78 (1) ◽  
pp. 99-147 ◽  
Author(s):  
C. Krattenthaler ◽  
Thomas W. Müller
Keyword(s):  
Hecke Groups

Normal Subgroups of Hecke Groups H(λ)

2009 ◽  
Vol 13 (2) ◽  
pp. 219-230 ◽  
Author(s):  
Özden Koruoğlu ◽  
Recep Sahin ◽  
Sebahattin İkikardes ◽  
Ismail Naci Cangül
Keyword(s):  
Normal Subgroups ◽  
Hecke Groups
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