scholarly journals NONVANISHING OF JACOBI POINCARÉ SERIES

2010 ◽  
Vol 89 (2) ◽  
pp. 165-179 ◽  
Author(s):  
SOUMYA DAS
Keyword(s):  
Exponential Type ◽  
Poincaré Series ◽  
Jacobi Forms ◽  
Poincare Series ◽  
Integer Weight

AbstractWe prove that, under suitable conditions, a Jacobi Poincaré series of exponential type of integer weight and matrix index does not vanish identically. For the classical Jacobi forms, we construct a basis consisting of the ‘first’ few Poincaré series, and also give conditions, both dependent on and independent of the weight, that ensure the nonvanishing of a classical Jacobi Poincaré series. We also obtain a result on the nonvanishing of a Jacobi Poincaré series when an odd prime divides the index.

Generators of Jacobi forms are Poincaré series

2016 ◽  
Vol 45 (3) ◽  
pp. 639-645
Author(s):  
Olav K. Richter ◽  
Howard Skogman
Keyword(s):  
Poincaré Series ◽  
Jacobi Forms ◽  
Poincare Series

scholarly journals Algebraicity of special L-values attached to Siegel–Jacobi modular forms

2020 ◽  
Author(s):  
Thanasis Bouganis ◽  
Jolanta Marzec
Keyword(s):  
Exponential Type ◽  
Modular Forms ◽  
Poincaré Series ◽  
Poincare Series ◽  
Jacobi Group ◽  
Doubling Method ◽  
Holomorphic Projection

Abstract In this work we obtain algebraicity results on special L-values attached to Siegel–Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a notion of near holomorphy for Siegel–Jacobi modular forms. Some of our results involve also holomorphic projection, which we obtain by using Siegel–Jacobi Poincaré series of exponential type.

scholarly journals EXACT FORMULAS FOR COEFFICIENTS OF JACOBI FORMS

2011 ◽  
Vol 07 (03) ◽  
pp. 825-833 ◽  
Author(s):  
KATHRIN BRINGMANN ◽  
OLAV K. RICHTER
Keyword(s):  
Fourier Coefficients ◽  
Theta Functions ◽  
Poincaré Series ◽  
Jacobi Forms ◽  
Mock Theta Functions ◽  
Explicit Formulas ◽  
Poincare Series ◽  
Real Analytic

In previous work, we introduced harmonic Maass–Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass–Jacobi–Poincaré series, as well as Zwegers' real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass–Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this paper, we give exact formulas for the Fourier coefficients of the holomorphic parts of harmonic Maass–Jacobi forms and, in particular, we obtain explicit formulas for the Fourier coefficients of weak Jacobi forms.

scholarly journals Poincaré series, 3d gravity and averages of rational CFT

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Viraj Meruliya ◽  
Sunil Mukhi ◽  
Palash Singh
Keyword(s):  
Poincaré Series ◽  
Simons Theory ◽  
Partition Functions ◽  
Moody Algebra ◽  
Modular Invariant ◽  
Poincare Series ◽  
Single Genus ◽  
3D Gravity ◽  
Chern Simons ◽  
Chern Simons Theory

Abstract We investigate the Poincaré series approach to computing 3d gravity partition functions dual to Rational CFT. For a single genus-1 boundary, we show that for certain infinite sets of levels, the SU(2)k WZW models provide unitary examples for which the Poincaré series is a positive linear combination of two modular-invariant partition functions. This supports the interpretation that the bulk gravity theory (a topological Chern-Simons theory in this case) is dual to an average of distinct CFT’s sharing the same Kac-Moody algebra. We compute the weights of this average for all seed primaries and all relevant values of k. We then study other WZW models, notably SU(N)1 and SU(3)k, and find that each class presents rather different features. Finally we consider multiple genus-1 boundaries, where we find a class of seed functions for the Poincaré sum that reproduces both disconnected and connected contributions — the latter corresponding to analogues of 3-manifold “wormholes” — such that the expected average is correctly reproduced.

Sign in / Sign up

Export Citation Format

Share Document