Matthew Greenberg[1] and Marco Adamo Seveso[2]
Formal period integrals and special value formulas
Pages: 217-237
Received: 12 January 2016
Accepted in revised form: 1 March 2016
Mathematics Subject Classification (2010): 11F67, 11F33.
Keywords: Special values of \(L\)-functions, \(p\)-adic \(L\)-Functions.
Author address:
[1] : University of Calgary, 2500 University Drive N.W., Calgary, T2N 1N4, Alberta, Canada
[2] : Università degli Studi di Milano, Via Cesare Saldini 50, Milano, 20133, Italy
Abstract: Motivated by the conjectures of Gan-Gross-Prasad, we develop a \(p\)-adic formalism for placing these conjectures in a \(p\)-adic setting which is suited for \(p\)-adic interpolation.
References
[1]
A. Ash and G. Stevens, \(p\)-adic deformations of arithmetic cohomology, submitted.
[2]
M. Bertolini and H. Darmon,
Hida families and rational points on elliptic curves,
Invent. Math. 168 (2007), no. 2, 371–431.
MR2289868
[3]
G. Chenevier, Familles \(p\)-adiques de formes automorphes pour \(\mathbf{GL}_n\),
J. Reine Angew. Math. 570 (2004), 143–217.
MR2075765
[4]
M. Greenberg and M. A. Seveso,
\(p\)-adic families of cohomological modualr forms for indefinite quaternion algebras and the Jacquet-Langlands correspondence,
Canad. J. Math., to appear, DOI: 10.4153/CJM-2015-062-x.
[5]
M. Greenberg and M. A. Seveso,
Triple product \(p\)-adic \(L\)-functions for balanced weights, preprint.
[6]
M. Greenberg and M. A. Seveso,
On the rationality of period integrals and special value formulas in the compact case, preprint.
[7]
M. Greenberg, M. A. Seveso and S. Shahabi,
Modular \(p\)-adic \(L\)-functions attached to real quadratic fields and arithmetic applications,
J. Reine Angew. Math., to appear,
DOI: 10.1515/crelle-2014-0088.
[8]
B.~H. Gross, Algebraic modular forms,
Israel J. Math. 113 (1999), 61–93.
MR1729443
[9]
Y. Liu, Refined Gan-Gross-Prasad conjecture for Bessel periods,
J. Reine Angew. Math., to appear,
DOI: 10.1515/crelle-2014-0016.
[10]
M. A. Seveso,
\(p\)-adic \(L\)-functions and the rationality of Darmon cycles,
Canad. J. Math. 64 (2012), no. 5, 1122–1181.
MR2979580
[11]
J.-L. Waldspurger,
Sur les valeurs de certaines fonctions \(L\) automorphes en leur centre de symétrie,
Compositio Math. 54 (1985), no. 2, 173–242.
MR0783511