---
_id: '53192'
abstract:
- lang: eng
text: The principal aim of this article is to attach and study $p$-adic
$L$-functions
to cohomological cuspidal automorphic representations $\Pi$
of $\operatorname
{GL}_{2n}$ over a totally
real field $F$
admitting a Shalika model. We use a modular symbol approach, along the global
lines of the work of Ash and Ginzburg, but our results are more definitive because
we draw heavily upon the methods used in the recent and separate works of all
three authors. By construction, our $p$-adic
$L$-functions
are distributions on the Galois group of the maximal abelian extension of $F$
unramified outside $p\infty$.
Moreover, we work under a weaker Panchishkine-type condition on $\Pi _p$
rather than the full ordinariness condition. Finally, we prove the so-called Manin
relations between the $p$-adic
$L$-functions
at all critical points. This has the striking consequence
that, given a unitary $\Pi$
whose standard $L$-function
admits at least two critical points, and given a prime $p$
such that $\Pi
_p$ is ordinary, the
central critical value $L(\frac {1}{2}, \Pi \otimes \chi )$
is non-zero for all except finitely many Dirichlet characters $\chi$
of $p$-power
conductor.
article_type: original
author:
- first_name: Mladen
full_name: Dimitrov, Mladen
last_name: Dimitrov
- first_name: Fabian
full_name: Januszewski, Fabian
id: '81636'
last_name: Januszewski
- first_name: A.
full_name: Raghuram, A.
last_name: Raghuram
citation:
ama: 'Dimitrov M, Januszewski F, Raghuram A. L-functions of GL(2n): p-adic properties
and non-vanishing of twists. Compositio Mathematica. 2021;156(12):2437-2468.
doi:10.1112/s0010437x20007551'
apa: 'Dimitrov, M., Januszewski, F., & Raghuram, A. (2021). L-functions of GL(2n):
p-adic properties and non-vanishing of twists. Compositio Mathematica,
156(12), 2437–2468. https://doi.org/10.1112/s0010437x20007551'
bibtex: '@article{Dimitrov_Januszewski_Raghuram_2021, title={L-functions of GL(2n):
p-adic properties and non-vanishing of twists}, volume={156}, DOI={10.1112/s0010437x20007551},
number={12}, journal={Compositio Mathematica}, publisher={Wiley}, author={Dimitrov,
Mladen and Januszewski, Fabian and Raghuram, A.}, year={2021}, pages={2437–2468}
}'
chicago: 'Dimitrov, Mladen, Fabian Januszewski, and A. Raghuram. “L-Functions of
GL(2n): P-Adic Properties and Non-Vanishing of Twists.” Compositio Mathematica
156, no. 12 (2021): 2437–68. https://doi.org/10.1112/s0010437x20007551.'
ieee: 'M. Dimitrov, F. Januszewski, and A. Raghuram, “L-functions of GL(2n): p-adic
properties and non-vanishing of twists,” Compositio Mathematica, vol. 156,
no. 12, pp. 2437–2468, 2021, doi: 10.1112/s0010437x20007551.'
mla: 'Dimitrov, Mladen, et al. “L-Functions of GL(2n): P-Adic Properties and Non-Vanishing
of Twists.” Compositio Mathematica, vol. 156, no. 12, Wiley, 2021, pp.
2437–68, doi:10.1112/s0010437x20007551.'
short: M. Dimitrov, F. Januszewski, A. Raghuram, Compositio Mathematica 156 (2021)
2437–2468.
date_created: 2024-04-03T16:58:55Z
date_updated: 2024-04-03T17:13:25Z
doi: 10.1112/s0010437x20007551
intvolume: ' 156'
issue: '12'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 2437-2468
publication: Compositio Mathematica
publication_identifier:
issn:
- 0010-437X
- 1570-5846
publication_status: published
publisher: Wiley
status: public
title: 'L-functions of GL(2n): p-adic properties and non-vanishing of twists'
type: journal_article
user_id: '81636'
volume: 156
year: '2021'
...
---
_id: '37672'
abstract:
- lang: eng
text: AbstractLet ${F}_{BC} (\lambda , k;
t)$ be the Heckman–Opdam
hypergeometric function of type BC with multiplicities $k= ({k}_{1} , {k}_{2}
, {k}_{3} )$ and weighted
half-sum $\rho (k)$
of positive roots. We prove that ${F}_{BC} (\lambda + \rho
(k), k; t)$ converges
as ${k}_{1} + {k}_{2} \rightarrow \infty $
and ${k}_{1} / {k}_{2} \rightarrow \infty $
to a function of type A for $t\in { \mathbb{R} }^{n}
$ and $\lambda \in { \mathbb{C}
}^{n} $. This limit
is obtained from a corresponding result for Jacobi polynomials of type BC, which
is proven for a slightly more general limit behavior of the multiplicities, using
an explicit representation of Jacobi polynomials in terms of Jack polynomials.
Our limits include limit transitions for the spherical functions of non-compact
Grassmann manifolds over one of the fields $ \mathbb{F} = \mathbb{R}
, \mathbb{C} , \mathbb{H} $
when the rank is fixed and the dimension tends to infinity. The limit functions
turn out to be exactly the spherical functions of the corresponding infinite-dimensional
Grassmann manifold in the sense of Olshanski.
author:
- first_name: Margit
full_name: Rösler, Margit
id: '37390'
last_name: Rösler
- first_name: Tom
full_name: Koornwinder, Tom
last_name: Koornwinder
- first_name: Michael
full_name: Voit, Michael
last_name: Voit
citation:
ama: Rösler M, Koornwinder T, Voit M. Limit transition between hypergeometric functions
of type BC and type A. Compositio Mathematica. 2013;149(8):1381-1400. doi:10.1112/s0010437x13007045
apa: Rösler, M., Koornwinder, T., & Voit, M. (2013). Limit transition between
hypergeometric functions of type BC and type A. Compositio Mathematica,
149(8), 1381–1400. https://doi.org/10.1112/s0010437x13007045
bibtex: '@article{Rösler_Koornwinder_Voit_2013, title={Limit transition between
hypergeometric functions of type BC and type A}, volume={149}, DOI={10.1112/s0010437x13007045},
number={8}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler,
Margit and Koornwinder, Tom and Voit, Michael}, year={2013}, pages={1381–1400}
}'
chicago: 'Rösler, Margit, Tom Koornwinder, and Michael Voit. “Limit Transition between
Hypergeometric Functions of Type BC and Type A.” Compositio Mathematica
149, no. 8 (2013): 1381–1400. https://doi.org/10.1112/s0010437x13007045.'
ieee: 'M. Rösler, T. Koornwinder, and M. Voit, “Limit transition between hypergeometric
functions of type BC and type A,” Compositio Mathematica, vol. 149, no.
8, pp. 1381–1400, 2013, doi: 10.1112/s0010437x13007045.'
mla: Rösler, Margit, et al. “Limit Transition between Hypergeometric Functions of
Type BC and Type A.” Compositio Mathematica, vol. 149, no. 8, Wiley, 2013,
pp. 1381–400, doi:10.1112/s0010437x13007045.
short: M. Rösler, T. Koornwinder, M. Voit, Compositio Mathematica 149 (2013) 1381–1400.
date_created: 2023-01-20T09:37:16Z
date_updated: 2023-01-24T22:15:13Z
department:
- _id: '555'
doi: 10.1112/s0010437x13007045
intvolume: ' 149'
issue: '8'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 1381-1400
publication: Compositio Mathematica
publication_identifier:
issn:
- 0010-437X
- 1570-5846
publication_status: published
publisher: Wiley
status: public
title: Limit transition between hypergeometric functions of type BC and type A
type: journal_article
user_id: '93826'
volume: 149
year: '2013'
...
---
_id: '39947'
author:
- first_name: Margit
full_name: Rösler, Margit
id: '37390'
last_name: Rösler
citation:
ama: Rösler M. Bessel convolutions on matrix cones. Compositio Mathematica.
2007;143(03):749-779. doi:10.1112/s0010437x06002594
apa: Rösler, M. (2007). Bessel convolutions on matrix cones. Compositio Mathematica,
143(03), 749–779. https://doi.org/10.1112/s0010437x06002594
bibtex: '@article{Rösler_2007, title={Bessel convolutions on matrix cones}, volume={143},
DOI={10.1112/s0010437x06002594},
number={03}, journal={Compositio Mathematica}, publisher={Wiley}, author={Rösler,
Margit}, year={2007}, pages={749–779} }'
chicago: 'Rösler, Margit. “Bessel Convolutions on Matrix Cones.” Compositio Mathematica
143, no. 03 (2007): 749–79. https://doi.org/10.1112/s0010437x06002594.'
ieee: 'M. Rösler, “Bessel convolutions on matrix cones,” Compositio Mathematica,
vol. 143, no. 03, pp. 749–779, 2007, doi: 10.1112/s0010437x06002594.'
mla: Rösler, Margit. “Bessel Convolutions on Matrix Cones.” Compositio Mathematica,
vol. 143, no. 03, Wiley, 2007, pp. 749–79, doi:10.1112/s0010437x06002594.
short: M. Rösler, Compositio Mathematica 143 (2007) 749–779.
date_created: 2023-01-25T09:55:18Z
date_updated: 2023-01-26T17:47:42Z
department:
- _id: '555'
doi: 10.1112/s0010437x06002594
extern: '1'
intvolume: ' 143'
issue: '03'
keyword:
- Algebra and Number Theory
language:
- iso: eng
page: 749-779
publication: Compositio Mathematica
publication_identifier:
issn:
- 0010-437X
- 1570-5846
publication_status: published
publisher: Wiley
status: public
title: Bessel convolutions on matrix cones
type: journal_article
user_id: '93826'
volume: 143
year: '2007'
...