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This article is cited in 24 scientific papers (total in 25 papers)
Non-Archimedean integration and Jacquet–Langlands $p$-adic $L$-functions
Yu. I. Manin
Abstract:
In 1964 Kubota and Leopoldt constructed a $p$-adic analogue of the Riemann zeta-function. Since then the class of $L$-functions with $p$-adic variants has continually been enlarged. At the beginning of the article we survey work in this direction, using the technique of the $p$-adic Mellin transform. Then we show how to apply it to the construction of non-Archimedean measures and integrals corresponding to parabolic forms relative to the Hilbert groups. The exposition is in the adele language of Jacquet and Langlands. We construct $p$-adic $L$-functions associated with representations of $GL(2)$ over completely real fields, of discrete type at infinity.
Received: 30.07.1975
Citation:
Yu. I. Manin, “Non-Archimedean integration and Jacquet–Langlands $p$-adic $L$-functions”, Russian Math. Surveys, 31:1 (1976), 5–57
Linking options:
https://www.mathnet.ru/eng/rm3639https://doi.org/10.1070/RM1976v031n01ABEH001444 https://www.mathnet.ru/eng/rm/v31/i1/p5
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Abstract page: | 867 | Russian version PDF: | 368 | English version PDF: | 48 | References: | 67 | First page: | 3 |
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