Motivic L-function (original) (raw)
In mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v acting on the v-inertial invariants of the v-adic realization of the motive. For infinite places, Jean-Pierre Serre gave a recipe in for the so-called Gamma factors in terms of the Hodge realization of the motive. It is conjectured that, like other L-functions, that each motivic L-function can be analytically continued to a meromorphic function on the entire complex plane and satisfies a functional equation relating the L-function L(s, M) of a motive M to L(1 − s, M∨), where M∨ is the dual of the motive M.
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| dbo:abstract | In mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v acting on the v-inertial invariants of the v-adic realization of the motive. For infinite places, Jean-Pierre Serre gave a recipe in for the so-called Gamma factors in terms of the Hodge realization of the motive. It is conjectured that, like other L-functions, that each motivic L-function can be analytically continued to a meromorphic function on the entire complex plane and satisfies a functional equation relating the L-function L(s, M) of a motive M to L(1 − s, M∨), where M∨ is the dual of the motive M. (en) |
| dbo:wikiPageExternalLink | http://sunsite.ubc.ca/DigitalMathArchive/Langlands/pdf/lfunct-ps.pdf https://web.archive.org/web/20160303210111/http:/mathunion.org/ICM/ICM1978.1/Main/icm1978.1.0165.0176.ocr.pdf http://mathunion.org/ICM/ICM1978.1/Main/icm1978.1.0165.0176.ocr.pdf https://www.ams.org/online_bks/pspum332/pspum332-ptIV-8.pdf http://www.numdam.org/item%3Fid=SDPP_1969-1970__11_2_A4_0 |
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| rdfs:comment | In mathematics, motivic L-functions are a generalization of Hasse–Weil L-functions to general motives over global fields. The local L-factor at a finite place v is similarly given by the characteristic polynomial of a Frobenius element at v acting on the v-inertial invariants of the v-adic realization of the motive. For infinite places, Jean-Pierre Serre gave a recipe in for the so-called Gamma factors in terms of the Hodge realization of the motive. It is conjectured that, like other L-functions, that each motivic L-function can be analytically continued to a meromorphic function on the entire complex plane and satisfies a functional equation relating the L-function L(s, M) of a motive M to L(1 − s, M∨), where M∨ is the dual of the motive M. (en) |
| rdfs:label | モチーフのL関数 (ja) Motivic L-function (en) |
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