Riv. Mat. Univ. Parma, Vol. 7, No. 1, 2016

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, 371431. MR2289868
[3] G. Chenevier, Familles \(p\)-adiques de formes automorphes pour \(\mathbf{GL}_n\), J. Reine Angew. Math. 570 (2004), 143217. 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), 6193. 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, 11221181. MR2979580
[11] J.-L. Waldspurger, Sur les valeurs de certaines fonctions \(L\) automorphes en leur centre de symétrie, Compositio Math. 54 (1985), no. 2, 173242. MR0783511


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