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Rigid-analytic L-transforms. (English) Zbl 0572.14014

Number theory, Proc. Journ. arith., Noordwijkerhout/Neth. 1983, Lect. Notes Math. 1068, 216-230 (1984).
[For the entire collection see Zbl 0535.00008.]
The author presents a new method of defining p-adic L-functions for a certain class of elliptic curves. In the first section, he reviews the general philosophy of complex and p-adic L-functions, and then he explains the idea of the method which is based on the notion of a rigid- analytic automorphic form. The construction of a p-adic L-function associated to such an automorphic form is carried out in the second section.
Reviewer: W.Lütkebohmert

MSC:

14G20 Local ground fields in algebraic geometry
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)

Citations:

Zbl 0535.00008