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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
scan of Zbl 0475.12018

Cited in 12 Reviews
Cited in 67 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
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\textit{H. M. Stark}, Adv. Math. 35, 197--235 (1980; Zbl 0475.12018)
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References:

[1] Birch, B. J., Diophantine Analysis and modular functions, (Algebraic Geometry (1969), Oxford Univ. Press: Oxford Univ. Press London/New York), 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] Helmut, Hasse, Neue Begründung der komplexen Multiplikation I, II, 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: 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 \(f_1, f_2, f_3, γ_2, γ_3\), Crelle, 286/287, 46-74 (1976) · Zbl 0335.12018
[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: 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: Tata Institute of Fundamental Research Bombay
[11] Stark, H. M., \(L\)-functions at \(s = 1\). I, II, III, 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, (Algebraic Number Fields (1977), Academic Press: Academic Press New York) · Zbl 0391.12006
[13] Weber, H., (Lehrbuch der Algebra, Vol. 3 (1961), Chelsea: Chelsea New York)
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