Coates, John On \(p\)-adic \(L\)-functions attached to motives over \(\mathbb Q\). II. (English) Zbl 0783.11040 Bol. Soc. Bras. Mat., Nova Sér. 20, No. 1, 101-112 (1989). 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. Reviewer: P.Bayer (Barcelona) Cited in 1 ReviewCited in 9 Documents 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 Keywords:existence of \(p\)-adic \(L\)-functions; motives; Euler factors Citations:Zbl 0783.11039 PDFBibTeX XMLCite \textit{J. Coates}, Bol. Soc. Bras. Mat., Nova Sér. 20, No. 1, 101--112 (1989; Zbl 0783.11040) Full Text: DOI 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.