P-adic L-functions and P-adic Representations

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American Mathematical Soc., 2000 - Mathematics - 150 pages
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Traditionally, $p$-adic $L$-functions have been constructed from complex $L$-functions via special values and Iwasawa theory. In this volume, Perrin-Riou presents a theory of $p$-adic $L$-functions coming directly from $p$-adic Galois representations (or, more generally, from motives). This theory encompasses, in particular, a construction of the module of $p$-adic $L$-functions via the arithmetic theory and a conjectural definition of the $p$-adic $L$-function via its special values. Since the original publication of this book in French (see Asterisque 229, 1995), the field has undergone significant progress. These advances are noted in this English edition. Also, some minor improvements have been made to the text.

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Construction of the module of padic Lfunctions without factors at infinity
Modules of padic Lfunctions of V
Values of the module of adic Lfunctions
The padic Lfunction of a motive

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