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On \(p\)-adic \(L\)-functions attached to motives over \(\mathbb Q\). II. (English) Zbl 0783.11040

This is a corrected version of a conjecture formulated by the author and B. Perrin-Riou in [Adv. Stud. Pure Math. 17, 23–54 (1989; Zbl 0783.11039)] about the existence of \(p\)-adic \(L\)-functions attached to motives over \(\mathbb Q\). Modifications of the Euler factors at \(\infty\) and at \(p\) of the complex \(L\)-series of the motif \(M\) produce a modification of the conjecture by a suitable power of \(i=\sqrt{-1}\). The normalizations are also changed in the sense that the critical point of the motif is supposed to be the point \(s=1\) instead of \(s=0\), as it was assumed in the former paper.

MSC:

11G40 \(L\)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture
11F33 Congruences for modular and \(p\)-adic modular forms
11F67 Special values of automorphic \(L\)-series, periods of automorphic forms, cohomology, modular symbols
11G09 Drinfel’d modules; higher-dimensional motives, etc.
11R23 Iwasawa theory

Citations:

Zbl 0783.11039
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References:

[1] Coates, J., Perrin-Riou, B., On p-adic L-functions attached to motives over \(\mathbb{Q}\), Advanced Studies in Pure Math.17 (1989), 23–54. · Zbl 0783.11039
[2] Deligne, P.,Les constantes des équations fonctionelles des fonctions L, Antwerp II, Lec. Notes in Math.349 (1973), 501–595. Springer-Verlag.
[3] –,Valeurs de fonctions L et périods d’intégrales, Proc. Symp. Pure Math. part 2,33 (1979), 313–346.
[4] Tate, J.,Number theoretic background, Proc. Symp. Pure Math. part 2,33 (1979), 3–26. · Zbl 0422.12007
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