On Eichler cohomology and on Eichler integrals

1974 ◽  
pp. 53-59
Author(s):  
Lipman Bers
Keyword(s):  
Eichler Cohomology ◽  
Eichler Integrals

Transcendental values of certain Eichler integrals

2011 ◽  
Vol 43 (5) ◽  
pp. 939-952 ◽  
Author(s):  
Sanoli Gun ◽  
M. Ram Murty ◽  
Purusottam Rath
Keyword(s):  
Eichler Integrals

PARABOLIC GENERALIZED MODULAR FORMS AND THEIR CHARACTERS

2009 ◽  
Vol 05 (05) ◽  
pp. 845-857 ◽  
Author(s):  
MARVIN KNOPP ◽  
GEOFFREY MASON
Keyword(s):  
Riemann Surface ◽  
Modular Form ◽  
Finite Index ◽  
Modular Forms ◽  
Modular Group ◽  
Compact Riemann Surface ◽  
Eichler Cohomology

We make a detailed study of the generalized modular forms of weight zero and their associated multiplier systems (characters) on an arbitrary subgroup Γ of finite index in the modular group. Among other things, we show that every generalized divisor on the compact Riemann surface associated to Γ is the divisor of a modular form (with unitary character) which is unique up to scalars. This extends a result of Petersson, and has applications to the Eichler cohomology.

EICHLER COHOMOLOGY THEOREM FOR VECTOR-VALUED MODULAR FORMS

2013 ◽  
Vol 09 (07) ◽  
pp. 1765-1788 ◽  
Author(s):  
JOSE GIMENEZ
Keyword(s):  
Modular Forms ◽  
Modular Group ◽  
Large Integer ◽  
Eichler Cohomology ◽  
Vector Valued

We prove the Eichler cohomology theorem for vector-valued modular forms of large integer weights on the full modular group.

scholarly journals ON THE QUANTUM INVARIANT FOR THE BRIESKORN HOMOLOGY SPHERES

2005 ◽  
Vol 16 (06) ◽  
pp. 661-685 ◽  
Author(s):  
KAZUHIRO HIKAMI
Keyword(s):  
Asymptotic Behavior ◽  
Irreducible Representation ◽  
Fundamental Group ◽  
Modular Form ◽  
Quantum Invariant ◽  
Exact Asymptotic Behavior ◽  
Chern Simons ◽  
Eichler Integrals ◽  
Limiting Value ◽  
Modular Property

We study an exact asymptotic behavior of the Witten–Reshetikhin–Turaev SU(2) invariant for the Brieskorn homology spheres Σ(p1, p2, p3) by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit τ → N ∈ ℤ. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern–Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.

scholarly journals Eichler integrals and harmonic weak Maass forms

2014 ◽  
Vol 411 (1) ◽  
pp. 429-441 ◽  
Author(s):  
Dohoon Choi ◽  
Byungchan Kim ◽  
Subong Lim
Keyword(s):  
Maass Forms ◽  
Eichler Integrals

scholarly journals Eichler integrals and string theory

1996 ◽  
Vol 37 (5) ◽  
pp. 2510-2526
Author(s):  
Leonidas Sandoval
Keyword(s):  
String Theory ◽  
Eichler Integrals
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