On the analogue of Weil's converse theorem for Jacobi forms and their lift to half-integral weight modular forms

Yves Martin; Denis Osses

doi:10.1007/s11139-010-9258-x

On the analogue of Weil's converse theorem for Jacobi forms and their lift to half-integral weight modular forms

Yves Martin
, Denis Osses

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

We generalize Weil's converse theorem to Jacobi cusp forms of weight k, index m and Dirichlet character χ over the group Γ₀(N)⋉ℤ². Then two applications of this result are given; we generalize a construction of Jacobi forms due to Skogman and present a new proof for several known lifts of such Jacobi forms to half-integral weight modular forms.

Original language	English
Pages (from-to)	155-183
Number of pages	29
Journal	Ramanujan Journal
Volume	26
Issue number	2
DOIs	https://doi.org/10.1007/s11139-010-9258-x
State	Published - Nov 2011
Externally published	Yes

Keywords

Dirichlet series
Functional equations
Jacobi forms

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10.1007/s11139-010-9258-x

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abstract = "We generalize Weil's converse theorem to Jacobi cusp forms of weight k, index m and Dirichlet character χ over the group Γ0(N)⋉ℤ2. Then two applications of this result are given; we generalize a construction of Jacobi forms due to Skogman and present a new proof for several known lifts of such Jacobi forms to half-integral weight modular forms.",

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author = "Yves Martin and Denis Osses",

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doi = "10.1007/s11139-010-9258-x",

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AU - Martin, Yves

AU - Osses, Denis

PY - 2011/11

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N2 - We generalize Weil's converse theorem to Jacobi cusp forms of weight k, index m and Dirichlet character χ over the group Γ0(N)⋉ℤ2. Then two applications of this result are given; we generalize a construction of Jacobi forms due to Skogman and present a new proof for several known lifts of such Jacobi forms to half-integral weight modular forms.

AB - We generalize Weil's converse theorem to Jacobi cusp forms of weight k, index m and Dirichlet character χ over the group Γ0(N)⋉ℤ2. Then two applications of this result are given; we generalize a construction of Jacobi forms due to Skogman and present a new proof for several known lifts of such Jacobi forms to half-integral weight modular forms.

KW - Dirichlet series

KW - Functional equations

KW - Jacobi forms

UR - https://www.scopus.com/pages/publications/80255136238

U2 - 10.1007/s11139-010-9258-x

DO - 10.1007/s11139-010-9258-x

M3 - Article

AN - SCOPUS:80255136238

SN - 1382-4090

VL - 26

SP - 155

EP - 183

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -

On the analogue of Weil's converse theorem for Jacobi forms and their lift to half-integral weight modular forms

Abstract

Keywords

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