A new proof to the period problems of GL(2)

Hengfei Lu

doi:10.1016/j.jnt.2017.03.010

A new proof to the period problems of GL(2)

Hengfei Lu

National University of Singapore

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

4 Scopus citations

Abstract

We use the relations among the base change representations, theta lifts and Whittaker models, to give a new proof to the period problems of GL(2) over a quadratic local field extension E/F. We classify both local and global D^×(F)-distinguished representations π^D of D^×(E), where D^× is an inner form of GL(2) defined over a nonarchimedean field or a number field F.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Journal of Number Theory
Volume	180
DOIs	https://doi.org/10.1016/j.jnt.2017.03.010
State	Published - Nov 2017
Externally published	Yes

Keywords

Inner forms
Periods
Theta lifts
Whittaker model

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10.1016/j.jnt.2017.03.010

Cite this

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title = "A new proof to the period problems of GL(2)",

abstract = "We use the relations among the base change representations, theta lifts and Whittaker models, to give a new proof to the period problems of GL(2) over a quadratic local field extension E/F. We classify both local and global D×(F)-distinguished representations πD of D×(E), where D× is an inner form of GL(2) defined over a nonarchimedean field or a number field F.",

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note = "Publisher Copyright: {\textcopyright} 2017 Elsevier Inc.",

year = "2017",

month = nov,

doi = "10.1016/j.jnt.2017.03.010",

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PY - 2017/11

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N2 - We use the relations among the base change representations, theta lifts and Whittaker models, to give a new proof to the period problems of GL(2) over a quadratic local field extension E/F. We classify both local and global D×(F)-distinguished representations πD of D×(E), where D× is an inner form of GL(2) defined over a nonarchimedean field or a number field F.

AB - We use the relations among the base change representations, theta lifts and Whittaker models, to give a new proof to the period problems of GL(2) over a quadratic local field extension E/F. We classify both local and global D×(F)-distinguished representations πD of D×(E), where D× is an inner form of GL(2) defined over a nonarchimedean field or a number field F.

KW - Inner forms

KW - Periods

KW - Theta lifts

KW - Whittaker model

UR - https://www.scopus.com/pages/publications/85019616710

U2 - 10.1016/j.jnt.2017.03.010

DO - 10.1016/j.jnt.2017.03.010

M3 - 文章

AN - SCOPUS:85019616710

SN - 0022-314X

VL - 180

SP - 1

EP - 25

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

A new proof to the period problems of GL(2)

Abstract

Keywords

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