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 |
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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.
In: Journal of the Institute of Mathematics of Jussieu, Vol. 18, No. 2, 01.03.2019, p. 347-447.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 -