Skip to main content Accessibility help
×
Home
Hostname: page-component-7ccbd9845f-9nx8b Total loading time: 0.256 Render date: 2023-01-29T10:55:27.054Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

ON THE FINE SPECTRAL EXPANSION OF JACQUET’S RELATIVE TRACE FORMULA

Published online by Cambridge University Press:  18 January 2006

Erez M. Lapid
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (erezla@math.huji.ac.il)

Abstract

The relative trace formula is a tool in the theory of automorphic forms which was invented by Jacquet in order to study period integrals and relate them to Langlands functoriality. In this paper we give an analogue of Arthur’s spectral expansion of the trace formula to the relative setup in the context of $\text{GL}_n$. This is an important step toward application of the relative trace formula and it extends earlier work by several authors to higher rank. Our method is new and based on complex analysis and majorization of Eisenstein series. To that end we use recent lower bounds of Brumley for Rankin–Selberg $L$-functions at the edge of the critical strip.

Type
Research Article
Copyright
2006 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
9
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

ON THE FINE SPECTRAL EXPANSION OF JACQUET’S RELATIVE TRACE FORMULA
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

ON THE FINE SPECTRAL EXPANSION OF JACQUET’S RELATIVE TRACE FORMULA
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

ON THE FINE SPECTRAL EXPANSION OF JACQUET’S RELATIVE TRACE FORMULA
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *