Journal of the Institute of Mathematics of Jussieu



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


Erez M. Lapid a1
a1 Einstein Institute of Mathematics, Edmond J. Safra Campus, Givat Ram, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (erezla@math.huji.ac.il)

Article author query
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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.

(Published Online January 18 2006)
(Received April 22 2004)
(Accepted March 15 2005)


Key Words: relative trace formula; Eisenstein series; $L$-functions.

Maths Classification

Primary 11F70; 11F72; Secondary 11F30; 11F67.