Whittaker rational structures and special values of the Asai L-function

Harald Grobner; Michael Harris; Erez Lapid

doi:10.1090/conm/664/13108

Whittaker rational structures and special values of the Asai L-function

Harald Grobner, Michael Harris, Erez Lapid

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Meeting Abstract › peer-review

Abstract

Let F be a totally real number field and E/F a totally imaginary quadratic extension of F. Let II be a cohomological, conjugate self-dual cuspidal automorphic representation of GL(n)(AE). Under a certain non-vanishing condition we relate the residue and the value of the Asai L-functions at s = 1 with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when n = 2, as well as a result of the first two named authors, both in the case F = Q.

Original language	English
Pages (from-to)	119-134
Number of pages	16
Journal	ADVANCES IN THE THEORY OF AUTOMORPHIC FORMS AND THEIR L-FUNCTIONS
Volume	664
DOIs	https://doi.org/10.1090/conm/664/13108
State	Published - 2016
Event	Workshop on Advances in the Theory of Automorphic Forms and their L-functions in honor of James Cogdell's 60th Birthday - Univ Vienna, Erwin Schrodinger Inst, Vienna, AUSTRIA Duration: 16 Oct 2013 → 25 Oct 2013

Access to Document

10.1090/conm/664/13108

https://ezproxy.weizmann.ac.il/login?url=http://dx.doi.org/10.1090/conm/664/13108

Cite this

@article{c4ebd1d7e7324a01b647fb7ce14d44af,

title = "Whittaker rational structures and special values of the Asai L-function",

abstract = "Let F be a totally real number field and E/F a totally imaginary quadratic extension of F. Let II be a cohomological, conjugate self-dual cuspidal automorphic representation of GL(n)(AE). Under a certain non-vanishing condition we relate the residue and the value of the Asai L-functions at s = 1 with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when n = 2, as well as a result of the first two named authors, both in the case F = Q.",

author = "Harald Grobner and Michael Harris and Erez Lapid",

year = "2016",

doi = "10.1090/conm/664/13108",

language = "الإنجليزيّة",

volume = "664",

pages = "119--134",

journal = "ADVANCES IN THE THEORY OF AUTOMORPHIC FORMS AND THEIR L-FUNCTIONS",

issn = "0271-4132",

publisher = "American Mathematical Society",

note = "Workshop on Advances in the Theory of Automorphic Forms and their L-functions in honor of James Cogdell's 60th Birthday ; Conference date: 16-10-2013 Through 25-10-2013",

}

TY - JOUR

T1 - Whittaker rational structures and special values of the Asai L-function

AU - Grobner, Harald

AU - Harris, Michael

AU - Lapid, Erez

PY - 2016

Y1 - 2016

N2 - Let F be a totally real number field and E/F a totally imaginary quadratic extension of F. Let II be a cohomological, conjugate self-dual cuspidal automorphic representation of GL(n)(AE). Under a certain non-vanishing condition we relate the residue and the value of the Asai L-functions at s = 1 with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when n = 2, as well as a result of the first two named authors, both in the case F = Q.

AB - Let F be a totally real number field and E/F a totally imaginary quadratic extension of F. Let II be a cohomological, conjugate self-dual cuspidal automorphic representation of GL(n)(AE). Under a certain non-vanishing condition we relate the residue and the value of the Asai L-functions at s = 1 with rational structures obtained from the cohomologies in top and bottom degrees via the Whittaker coefficient map. This generalizes a result in Eric Urban's thesis when n = 2, as well as a result of the first two named authors, both in the case F = Q.

U2 - 10.1090/conm/664/13108

DO - 10.1090/conm/664/13108

M3 - موجز برنامج المؤتمر

SN - 0271-4132

VL - 664

SP - 119

EP - 134

JO - ADVANCES IN THE THEORY OF AUTOMORPHIC FORMS AND THEIR L-FUNCTIONS

JF - ADVANCES IN THE THEORY OF AUTOMORPHIC FORMS AND THEIR L-FUNCTIONS

T2 - Workshop on Advances in the Theory of Automorphic Forms and their L-functions in honor of James Cogdell's 60th Birthday

Y2 - 16 October 2013 through 25 October 2013

ER -

Whittaker rational structures and special values of the Asai L-function

Abstract

Access to Document

Fingerprint

Cite this