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Imaginary Abelian number fields with class number one. (English) Zbl 0248.12007


MSC:

11R23 Iwasawa theory
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[1] N. C. ANKENY, S. CHOWLA AND H. HASSE, On the class number of the maximal real subfield of a cyclotomic field, J. fur Math., 217 (1965). · Zbl 0128.03501 · doi:10.1515/crll.1965.217.217
[2] E. ARTIN AND J. TATE, Class field theory, Benjamin · Zbl 0176.33504
[3] A. BAKER, Imaginary quadratic fields with class number 2, Ann. Math., 94 (1971) · Zbl 0219.12008 · doi:10.2307/1970739
[4] H. HASSE, ber die Klassenzahl abelscher Zahlkrper, Akademie Verlag, 1952
[5] K. ISEKI, On the imaginary quadratic fields of class number one or two, Japanese J., 21 (1951). · Zbl 0054.02301
[6] E. LANDAU, Abschatzungen von Charaktersummen, Einheiten und Klassenzahlen, Gt tingen Nachr., 1918. · JFM 46.0266.02
[7] M. E. Low, Real zeros of the Dedekind zeta function of an imaginary quadratic field, Acta Arithm., 14 (1968). · Zbl 0207.05602
[8] T. METSANKYLA, Zero-free regions of Dirichlet’s L-functions near the point 1, Ann. Univ Turku, 1970.
[9] G. POLYA, ber die Verteilung der quadratischen Reste und Nichtreste, Gttinge Nachr., 1918. · JFM 46.0266.01
[10] H. M. STARK, A transcendence theorem for class-number problems, Ann. Math., 9 (1971). JSTOR: · Zbl 0229.12010 · doi:10.2307/1970740
[11] T. TATUZAWA, On a theorem of Siegel, Japanese J., 21 (1951) · Zbl 0054.02302
[12] K. UCHIDA, Class numbers of imaginary abelian number fields I, Thoku Math. J., 2 (1971). · Zbl 0213.06903 · doi:10.2748/tmj/1178242689
[13] K. UCHIDA, Class numbers of imaginary abelian number fields II, Thoku Math. J., 2 (1971). · Zbl 0307.12007
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