Werner Müller & Sug Woo Shin 
Relative Trace Formulas [PDF ebook] 

A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.

Table of Content

​Archimedean theory and ǫ-factors for the Asai Rankin-Selberg integrals.- The relative trace formula in analytic number theory.- Dimensions of automorphic representations, L-functions and liftings.- Relative character identities and theta correspondence.- Incoherent definite spaces and Shimura varieties.- Shimura varieties for unitary groups and the doubling method.- Bessel decents and branching problems.- Distinguished representations of SO(n + 1, 1)×SO(n, 1), periods and branching laws.- Explicit decomposition of certain induced representations of the general linear group.- Mixed arithmetic theta lifting for unitary groups.- Twists of GL(3) L-functions.- Modular forms on G2 and their standard L-functions.

About the author

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Werner Müller is Professor Emeritus at the Mathematical Institute of the University of Bonn.  His research interests include geometric analysis, scattering theory, analytic theory of automorphic forms, and harmonic analysis on locally symmetric spaces. His work has been published in many journals, including Annals of Mathematics,  
Inventiones Mathematicae, Geometric and Functional Analysis, and 
Communications in Mathematical Physics.


Sug Woo Shin is Professor of Mathematics at the University of California at Berkeley. His research is centered on number theory, Shimura varieties, Langlands functoriality, trace formula, and automorphic forms. His work has appeared in many journals, including
Inventiones Mathematicae,
Mathematische Annalen, and the
Israel Journal of Mathematics.


Nicolas Templier is Associate Professor of Mathematics at Cornell University. His work focuses on number theory, automorphic forms, arithmetic geometry, ergodic theory, and mathematical physics. His list of publications include articles in
Inventiones Mathematicae, the
Ramanujan Journal, and the
Israel Journal of Mathematics.