Fourier–Jacobi periods of classical Saito–Kurokawa lifts

Hang Xue

doi:10.1007/s11139-016-9829-6

Fourier–Jacobi periods of classical Saito–Kurokawa lifts

Hang Xue

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

2 Scopus citations

Abstract

Kohnen–Skoruppa (Invent Math 95(3): 541–558, 1989) proved a formula for the ratio of the Petersson inner products of the half integral weight modular form and its Saito–Kurokawa lifting. We give an interpretation of this formula in the framework of the refined Gan–Gross–Prasad conjecture. This provides us with an example of the refined Gan–Gross–Prasad conjecture for the nontempered representations.

Original language	English (US)
Pages (from-to)	111-139
Number of pages	29
Journal	Ramanujan Journal
Volume	45
Issue number	1
DOIs	https://doi.org/10.1007/s11139-016-9829-6
State	Published - Jan 1 2018
Externally published	Yes

Keywords

Fourier–Jacobi periods
Gan–Gross–Prasad conjecture
Saito–Kurokawa lifts

ASJC Scopus subject areas

Algebra and Number Theory

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10.1007/s11139-016-9829-6

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title = "Fourier–Jacobi periods of classical Saito–Kurokawa lifts",

abstract = "Kohnen–Skoruppa (Invent Math 95(3): 541–558, 1989) proved a formula for the ratio of the Petersson inner products of the half integral weight modular form and its Saito–Kurokawa lifting. We give an interpretation of this formula in the framework of the refined Gan–Gross–Prasad conjecture. This provides us with an example of the refined Gan–Gross–Prasad conjecture for the nontempered representations.",

keywords = "Fourier–Jacobi periods, Gan–Gross–Prasad conjecture, Saito–Kurokawa lifts",

author = "Hang Xue",

note = "Funding Information: This material is based upon work supported by the National Science Foundation under agreement No. DMS-1128115. Publisher Copyright: {\textcopyright} 2016, Springer Science+Business Media New York.",

year = "2018",

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doi = "10.1007/s11139-016-9829-6",

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T1 - Fourier–Jacobi periods of classical Saito–Kurokawa lifts

AU - Xue, Hang

N1 - Funding Information: This material is based upon work supported by the National Science Foundation under agreement No. DMS-1128115. Publisher Copyright: © 2016, Springer Science+Business Media New York.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - Kohnen–Skoruppa (Invent Math 95(3): 541–558, 1989) proved a formula for the ratio of the Petersson inner products of the half integral weight modular form and its Saito–Kurokawa lifting. We give an interpretation of this formula in the framework of the refined Gan–Gross–Prasad conjecture. This provides us with an example of the refined Gan–Gross–Prasad conjecture for the nontempered representations.

AB - Kohnen–Skoruppa (Invent Math 95(3): 541–558, 1989) proved a formula for the ratio of the Petersson inner products of the half integral weight modular form and its Saito–Kurokawa lifting. We give an interpretation of this formula in the framework of the refined Gan–Gross–Prasad conjecture. This provides us with an example of the refined Gan–Gross–Prasad conjecture for the nontempered representations.

KW - Fourier–Jacobi periods

KW - Gan–Gross–Prasad conjecture

KW - Saito–Kurokawa lifts

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JO - Ramanujan Journal

JF - Ramanujan Journal

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IS - 1

ER -

Fourier–Jacobi periods of classical Saito–Kurokawa lifts

Abstract

Keywords

ASJC Scopus subject areas

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