TY - JOUR
T1 - P-ADIC L-FUNCTIONS for UNITARY GROUPS
AU - Eischen, Ellen
AU - Harris, Michael
AU - Li, Jianshu
AU - Skinner, Christopher
N1 - Funding Information:
The authors are grateful for support from several funding sources. E.E.’s research was partially supported by National Science Foundation Grants DMS-1751281, DMS-1559609, and DMS-1249384. During an early part of the project, her research was partially supported by an AMS-Simons Travel Grant. M.H.’s research received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement no. 290766 (AAMOT). M.H. was partially supported by NSF Grant DMS-1404769. J.L.’s research was partially supported by RGC-GRF grant 16303314 of HKSAR. C.S.’s research was partially supported by National Science Foundation Grants DMS-0758379 and DMS-1301842.
Publisher Copyright:
© 2020 Journal of Materials Research. All rights reserved.
PY - 2020
Y1 - 2020
N2 - This paper completes the construction of -adic -functions for unitary groups. More precisely, in Harris, Li and Skinner ['-adic -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure', Doc. Math.Extra Vol. (2006), 393-464 (electronic)], three of the authors proposed an approach to constructing such -adic -functions (Part I). Building on more recent results, including the first named author's construction of Eisenstein measures and -adic differential operators [Eischen, 'A -adic Eisenstein measure for unitary groups', J. Reine Angew. Math.699 (2015), 111-142; '-adic differential operators on automorphic forms on unitary groups', Ann. Inst. Fourier (Grenoble)62(1) (2012), 177-243], Part II of the present paper provides the calculations of local -integrals occurring in the Euler product (including at). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.
AB - This paper completes the construction of -adic -functions for unitary groups. More precisely, in Harris, Li and Skinner ['-adic -functions for unitary Shimura varieties. I. Construction of the Eisenstein measure', Doc. Math.Extra Vol. (2006), 393-464 (electronic)], three of the authors proposed an approach to constructing such -adic -functions (Part I). Building on more recent results, including the first named author's construction of Eisenstein measures and -adic differential operators [Eischen, 'A -adic Eisenstein measure for unitary groups', J. Reine Angew. Math.699 (2015), 111-142; '-adic differential operators on automorphic forms on unitary groups', Ann. Inst. Fourier (Grenoble)62(1) (2012), 177-243], Part II of the present paper provides the calculations of local -integrals occurring in the Euler product (including at). Part III of the present paper develops the formalism needed to pair Eisenstein measures with Hida families in the setting of the doubling method.
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U2 - 10.1017/fmp.2020.4
DO - 10.1017/fmp.2020.4
M3 - Article
AN - SCOPUS:85084807550
VL - 8
JO - Forum of Mathematics, Pi
JF - Forum of Mathematics, Pi
SN - 2050-5086
M1 - e9
ER -