### Abstract

For the group we perform a comparison between two relative trace formulas: On the one hand, the relative trace formula of Jacquet for the quotient , where is a nontrivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to nonstandard test functions. This gives a new proof of the celebrated result of Waldspurger on toric periods, and suggests a new way of comparing trace formulas, with some analogies to Langlands' 'Beyond Endoscopy' program.

Original language | English (US) |
---|---|

Pages (from-to) | 347-447 |

Number of pages | 101 |

Journal | Journal of the Institute of Mathematics of Jussieu |

Volume | 18 |

Issue number | 2 |

DOIs | |

State | Published - Mar 1 2019 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)

### Keywords

- L-functions
- Waldspurger's formula
- beyond endoscopy
- periods
- relative trace formula

### Cite this

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**Beyond endoscopy for the relative trace formula II : Global theory.** / Sakellaridis, Yiannis.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Beyond endoscopy for the relative trace formula II

T2 - Global theory

AU - Sakellaridis, Yiannis

PY - 2019/3/1

Y1 - 2019/3/1

N2 - For the group we perform a comparison between two relative trace formulas: On the one hand, the relative trace formula of Jacquet for the quotient , where is a nontrivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to nonstandard test functions. This gives a new proof of the celebrated result of Waldspurger on toric periods, and suggests a new way of comparing trace formulas, with some analogies to Langlands' 'Beyond Endoscopy' program.

AB - For the group we perform a comparison between two relative trace formulas: On the one hand, the relative trace formula of Jacquet for the quotient , where is a nontrivial torus, and on the other the Kuznetsov trace formula (involving Whittaker periods), applied to nonstandard test functions. This gives a new proof of the celebrated result of Waldspurger on toric periods, and suggests a new way of comparing trace formulas, with some analogies to Langlands' 'Beyond Endoscopy' program.

KW - L-functions

KW - Waldspurger's formula

KW - beyond endoscopy

KW - periods

KW - relative trace formula

UR - http://www.scopus.com/inward/record.url?scp=85018810227&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85018810227&partnerID=8YFLogxK

U2 - 10.1017/S1474748017000032

DO - 10.1017/S1474748017000032

M3 - Article

AN - SCOPUS:85018810227

VL - 18

SP - 347

EP - 447

JO - Journal of the Institute of Mathematics of Jussieu

JF - Journal of the Institute of Mathematics of Jussieu

SN - 1474-7480

IS - 2

ER -