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

Published online by Cambridge University Press:  18 January 2006

Erez M. Lapid
Erez M. Lapid
Affiliation:
Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel ([email protected])
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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.

Keywords

relative trace formulaEisenstein series$L$-functionsPrimary 11F7011F72Secondary 11F3011F67
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 5 , Issue 2 , April 2006 , pp. 263 - 308
Copyright
2006 Cambridge University Press

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