Bombieri, Enrico The Rosetta stone of \(L\)-functions. (English) Zbl 1171.11321 Int. Math. Nachr., Wien 196, 1-14 (2004). This is a survey on motivic \(L\)-functions, associated to algebraic varieties over number fields, Artin \(L\)-functions, associated to finite dimensional representations of the absolute Galois group of a number field, and automorphic \(L\)-functions, associated to automorphic forms on algebraic groups modulo discrete subgroups. Conjecturally, the three classes are equal, but this is known only in very few cases. Reviewer: Florin Nicolae (Berlin) Cited in 1 Review MSC: 11M41 Other Dirichlet series and zeta functions 11F66 Langlands \(L\)-functions; one variable Dirichlet series and functional equations 14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) 11R42 Zeta functions and \(L\)-functions of number fields Keywords:motivic L-functions; Artin L-functions; automorphic L-functions PDFBibTeX XMLCite \textit{E. Bombieri}, Int. Math. Nachr., Wien 196, 1--14 (2004; Zbl 1171.11321)