scholarly journals Threshold corrections, generalised prepotentials and Eichler integrals

2015 ◽  
Vol 897 ◽  
pp. 781-820 ◽  
Author(s):  
Carlo Angelantonj ◽  
Ioannis Florakis ◽  
Boris Pioline
Keyword(s):  
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

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

scholarly journals Poincaré series and Eichler integrals

2009 ◽  
Vol 53 (3) ◽  
pp. 883-897 ◽  
Author(s):  
Wladimir de Azevedo Pribitkin
Keyword(s):  
Poincaré Series ◽  
Poincare Series ◽  
Eichler Integrals

scholarly journals On Periods of Meromorphic Eichler Integrals

1975 ◽  
Vol 57 ◽  
pp. 1-26
Author(s):  
Hiroki Sato
Keyword(s):  
Fuchsian Group ◽  
Kleinian Groups ◽  
Cohomology Groups ◽  
Finitely Generated ◽  
Eichler Integrals

In this paper we treat cohomology groups H1(G, C2q-1, M) of meromorphic Eichler integrals for a finitely generated Fuchsian group G of the first kind. According to L. V. Ahlfors [2] and L. Bers [4], H1(G, C2q-1, M) is the space of periods of meromorphic Eichler integrals for G. In the previous paper [8], we had period relations and inequalities of holomorphic Eichler integrals for a certain Kleinian groups.

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