Relative Trace Formulas

1. Front Matter

   Pages i-xvi

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2. Archimedean Theory and 𝜖-Factors for the Asai Rankin-Selberg Integrals

   • Raphaël Beuzart-Plessis

   Pages 1-50

3. The Relative Trace Formula in Analytic Number Theory

   • Valentin Blomer

   Pages 51-73

4. Dimensions of Automorphic Representations, L-Functions and Liftings

   • Solomon Friedberg, David Ginzburg

   Pages 75-100

5. Relative Character Identities and Theta Correspondence

   • Wee Teck Gan, Xiaolei Wan

   Pages 101-186

6. Incoherent Definite Spaces and Shimura Varieties

   • Benedict H. Gross

   Pages 187-215

7. Shimura Varieties for Unitary Groups and the Doubling Method

   • Michael Harris

   Pages 217-251

8. Bessel Descents and Branching Problems

   • Dihua Jiang, Lei Zhang

   Pages 253-290

9. Distinguished Representations of SO(n + 1,  1) × SO(n,  1), Periods and Branching Laws

   • Toshiyuki Kobayashi, Birgit Speh

   Pages 291-320

10. Explicit Decomposition of Certain Induced Representations of the General Linear Group

    • Erez Lapid

    Pages 321-327

11. Mixed Arithmetic Theta Lifting for Unitary Groups

    • Yifeng Liu

    Pages 329-350

12. Twists of GL(3) L-functions

    • Ritabrata Munshi

    Pages 351-378

13. Modular forms on G ₂ and their Standard L-Function

    • Aaron Pollack

    Pages 379-427

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.

• L-functions
• automorphic forms
• Simons Symposia
• trace formula
• automorphic representations
• theta correspondence
• Shimura varieties
• theta lifting
• Bessel decents
• modular forms

• Mathematical Institute, University of Bonn, Bonn, Germany

  Werner Müller

• Department of Mathematics, University of California, Berkeley, USA

  Sug Woo Shin

• Department of Mathematics, Malott Hall, Cornell University, Ithaca, USA

  Nicolas Templier

​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.

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