1,818 research outputs found
L-functions for holomorphic forms on GSp(4) x GL(2) and their special values
We provide an explicit integral representation for L-functions of pairs (F,g)
where F is a holomorphic genus 2 Siegel newform and g a holomorphic elliptic
newform, both of squarefree levels and of equal weights. When F,g have level
one, this was earlier known by the work of Furusawa. The extension is not
straightforward. Our methods involve precise double-coset and volume
computations as well as an explicit formula for the Bessel model for GSp(4) in
the Steinberg case; the latter is possibly of independent interest. We apply
our integral representation to prove an algebraicity result for a critical
special value of L(s, F \times g). This is in the spirit of known results on
critical values of triple product L-functions, also of degree 8, though there
are significant differences.Comment: 48 pages, typos corrected, some changes in Sections 6 and 7, other
minor change
Pullbacks of Eisenstein series from GU(3,3) and critical L-values for GSp(4) X GL(2)
Let F be a genus two Siegel newform and g a classical newform, both of
squarefree levels and of equal weight l. We prove a pullback formula for
certain Eisenstein series -- thus generalizing a construction of Shimura -- and
use this to derive an explicit integral representation for the degree eight
L-function L(s, F X g). This integral representation involves the pullback of a
simple Siegel-type Eisenstein series on the unitary group GU(3,3). As an
application, we prove a reciprocity law -- predicted by Deligne's conjecture --
for the critical special values L(m, F X g) where m is an integer, 2 <= m <=
l/2-1.Comment: 45 pages; Some notational changes made, inaccuracies eliminated and
typos fixed in accordance with an anonymous referee's helpful comments. To
appear in the Pacific Journal of Mathematic
On ratios of Petersson norms for Yoshida lifts
We prove an algebraicity property for a certain ratio of Petersson norms
associated to a Siegel cusp form of degree 2 (and arbitrary level) whose
adelization generates a weak endoscopic lift. As a preparation for this, we
explicate various features of the correspondence between scalar valued Siegel
cusp forms of degree n and automorphic representations on GSp_{2n}.Comment: Several minor changes; 34 page
On sup-norms of cusp forms of powerful level
Let f be an L^2-normalized Hecke--Maass cuspidal newform of level N and
Laplace eigenvalue \lambda. It is shown that |f|_\infty <<_{\lambda, \epsilon}
N^{-1/12 + \epsilon} for any \epsilon>0. The exponent is further improved in
the case when N is not divisible by "small squares". Our work extends and
generalizes previously known results in the special case of N squarefree.Comment: Final version, to appear in JEMS. Please also note that the results
of this paper have been significantly improved in my recent paper
arXiv:1509.07489 which uses a fairly different methodolog
Hybrid sup-norm bounds for Maass newforms of powerful level
Let be an -normalized Hecke--Maass cuspidal newform of level ,
character and Laplace eigenvalue . Let denote the
smallest integer such that and denote the largest integer such
that . Let denote the conductor of and define . In this paper, we prove the bound
,
which generalizes and strengthens previously known upper bounds for
.
This is the first time a hybrid bound (i.e., involving both and
) has been established for in the case of non-squarefree
. The only previously known bound in the non-squarefree case was in the
N-aspect; it had been shown by the author that provided . The present result significantly
improves the exponent of in the above case. If is a squarefree integer,
our bound reduces to , which was previously proved by Templier.
The key new feature of the present work is a systematic use of p-adic
representation theoretic techniques and in particular a detailed study of
Whittaker newforms and matrix coefficients for where is a local
field.Comment: Postprint version; to appear in Algebra and Number Theor
Phase Structure of Higher Spin Black Holes
We revisit the study of the phase structure of higher spin black holes
carried out in arXiv using the "canonical formalism". In particular
we study the low as well as high temperature regimes. We show that the
Hawking-Page transition takes place in the low temperature regime. The
thermodynamically favoured phase changes from conical surplus to black holes
and then again to conical surplus as we increase temperature. We then show that
in the high temperature regime the diagonal embedding gives the appropriate
description. We also give a map between the parameters of the theory near the
IR and UV fixed points. This makes the "good" solutions near one end map to the
"bad" solutions near the other end and vice versa.Comment: References added, Conclusions written in better manner, overall
exposition improved, version accepted in JHE
- …