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Constructions of p-adic L-functions and admissible measures for Hermitian modular forms. Pantchichkine, Alexei
Description
For a prime p and a positive integer n, the standard zeta function LF (s) is consid-
ered, attached to an Hermitian modular form F = â A(H)qH on the Hermitian upper half H
plane Hm of degree n, where H runs through semi-integral positive definite Hermitian matrices of degree n, i.e. H â Î m(O) over the integers O of an imaginary quadratic field K, where qH = exp(2Ï iTr(HZ)). Analytic p-adic continuation of their zeta functions constructed by A.Bouganis in the ordinary case, is extended to the admissible case via growing p-adic measures. Previously this problem was solved for the Siegel modular forms. Main result is stated in terms of the Hodge polygon PH(t) : [0,d] â R and the Newton polygon PN(t) = PN,p(t) : [0,d] â R of the zeta function LF (s) of degree d = 4n. Main theorem gives a p-adic analytic interpolation of the L values in the form of certain integrals with respect to Mazur-type measures.
<br/>
Related references: <br/>
[BS00] B Ì ocherer, S., and Schmidt, C.-G., p-adic measures attached to Siegel modular forms,
Ann. Inst. Fourier 50, N. 5, 1375â 1443 (2000).
<br/>
[Bou16] Bouganis T., p-adic Measures for Hermitian Modular Forms and the Rankinâ Selberg
Method. in Elliptic Curves, Modular Forms and Iwasawa Theory â Conference in honour of the 70th birthday of John Coates, pp 33â 86
<br/>
[CourPa] Courtieu M, Panchishkin A. A, Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms, Lecture Notes in Mathematics 1471, Springer-Verlag, 2004 (2nd augmented ed.)
Item Metadata
Title |
Constructions of p-adic L-functions and admissible measures for Hermitian modular forms.
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2018-10-02T15:32
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Description |
For a prime p and a positive integer n, the standard zeta function LF (s) is consid-
ered, attached to an Hermitian modular form F = â A(H)qH on the Hermitian upper half H
plane Hm of degree n, where H runs through semi-integral positive definite Hermitian matrices of degree n, i.e. H â Î m(O) over the integers O of an imaginary quadratic field K, where qH = exp(2Ï iTr(HZ)). Analytic p-adic continuation of their zeta functions constructed by A.Bouganis in the ordinary case, is extended to the admissible case via growing p-adic measures. Previously this problem was solved for the Siegel modular forms. Main result is stated in terms of the Hodge polygon PH(t) : [0,d] â R and the Newton polygon PN(t) = PN,p(t) : [0,d] â R of the zeta function LF (s) of degree d = 4n. Main theorem gives a p-adic analytic interpolation of the L values in the form of certain integrals with respect to Mazur-type measures.
<br/> Related references: <br/> [BS00] B Ì ocherer, S., and Schmidt, C.-G., p-adic measures attached to Siegel modular forms, Ann. Inst. Fourier 50, N. 5, 1375â 1443 (2000). <br/> [Bou16] Bouganis T., p-adic Measures for Hermitian Modular Forms and the Rankinâ Selberg Method. in Elliptic Curves, Modular Forms and Iwasawa Theory â Conference in honour of the 70th birthday of John Coates, pp 33â 86 <br/> [CourPa] Courtieu M, Panchishkin A. A, Non-Archimedean L-Functions and Arithmetical Siegel Modular Forms, Lecture Notes in Mathematics 1471, Springer-Verlag, 2004 (2nd augmented ed.) |
Extent |
59.0
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Université Grenoble Alpes
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Series | |
Date Available |
2019-04-01
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0377712
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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DSpace
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Attribution-NonCommercial-NoDerivatives 4.0 International