Stark, Harold M. \(L\)-functions at \(s=1\). IV: First derivatives at \(s=0\). (English) Zbl 0475.12018 Adv. Math. 35, 197-235 (1980). Reviewer: Lawrence G. Roberts Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 12 ReviewsCited in 63 Documents MSC: 11R42 Zeta functions and \(L\)-functions of number fields 11M41 Other Dirichlet series and zeta functions Keywords:complex multiplication; units; evaluation of derivative of L-functions; reciprocity; totally real extension; number of roots of unity; class field Citations:Zbl 0263.10015; Zbl 0316.12007; Zbl 0348.12017; Zbl 0221.10029 PDF BibTeX XML Cite \textit{H. M. Stark}, Adv. Math. 35, 197--235 (1980; Zbl 0475.12018) Full Text: DOI OpenURL References: [1] Birch, B.J, Diophantine analysis and modular functions, (), 35-42 · Zbl 0246.10017 [2] Coates, J; Wiles, A, On the conjecture of Birch and Swinnerton-Dyer, Invent. math., 39, 223-251, (1977) · Zbl 0359.14009 [3] Hasse, Helmut; Helmut, Hasse, Neue begründung der komplexen multiplikation I, II, Crelle, Crelle, 165, 64-88, (1931) · Zbl 0002.12002 [4] Kenku, M.A, On the L-function of quadratic forms, Crelle, 276, 36-43, (1975) · Zbl 0305.10020 [5] Lang, S, Elliptic functions, (1973), Addison-Wesley Reading, Mass [6] Robert, G, Unités elliptiques, Bull. soc. math. France, No. 36, (1973) [7] Schertz, Reinhard, Die singulären werte der weberschen funktionen f_{1}, f2, f3, γ2, γ3, Crelle, 286/287, 46-74, (1976) [8] Schertz, Reinhard, L-reihen in imaginär-quadratischen zahlkörpern und ihre anwendung auf klassenzahlprobleme bei quadratischen und biquadratischen zahlkörpern, I, Crelle, 262/263, 120-133, (1973) · Zbl 0285.12015 [9] Shimura, G, Introduction to the arithmetic theory of automorphic functions, (1971), Iwanami Shoten Tokyo, and Princeton Univ. Press, Princeton, N.J. · Zbl 0221.10029 [10] Siegel, C.L, Lectures on advanced analytic number theory, (1961), Tata Institute of Fundamental Research Bombay [11] Stark, H.M; Stark, H.M; Stark, H.M, L-functions at s = 1. I, II, III, Advances in math., Advances in math., Advances in math., 22, 64-84, (1976) · Zbl 0348.12017 [12] Stark, H.M, Class fields for real quadratic fields and L-series at 1, () · Zbl 0391.12006 [13] Weber, H, () 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.