Imaginary quadratic fields with small odd class number
Steven Arno ; M. L. Robinson ; Ferrell S. Wheeler
Acta Arithmetica, Tome 84 (1998), p. 295-330 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)
Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:207125 
@article{bwmeta1.element.bwnjournal-article-aav83i4p295bwm,
     author = {Steven Arno and M. L. Robinson and Ferrell S. Wheeler},
     title = {Imaginary quadratic fields with small odd class number},
     journal = {Acta Arithmetica},
     volume = {84},
     year = {1998},
     pages = {295-330},
     zbl = {0904.11031},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav83i4p295bwm}
}

Steven Arno; M. L. Robinson; Ferrell S. Wheeler. Imaginary quadratic fields with small odd class number. Acta Arithmetica, Tome 84 (1998) pp. 295-330. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav83i4p295bwm/

[000] [1] S. Arno, The imaginary quadratic fields of class number 4, Acta Arith. 60 (1992), 321-334. | Zbl 0760.11033

[001] [2] A. Baker, Linear forms in the logarithms of algebraic numbers. I, Mathematika 13 (1966), 204-216. | Zbl 0161.05201

[002] [3] A. Baker, Imaginary quadratic fields with class number 2, Ann. of Math. 94 (1971), 139-152.

[003] [4] A. Baker, Transcendental Number Theory, Cambridge Univ. Press, New York, 1975. | Zbl 0297.10013

[004] [5] B. J. Birch and H. P. F. Swinnerton-Dyer, Notes on elliptic curves. II, J. Reine Angew. Math. 218 (1965), 79-108. | Zbl 0147.02506

[005] [6] D. A. Buell, Class groups of quadratic fields. II, Math. Comp. 48 (1987), 85-93. | Zbl 0606.12004

[006] [7] H. Davenport, Multiplicative Number Theory, 2nd ed., Grad. Texts in Math. 74, Springer, New York, 1980. | Zbl 0453.10002

[007] [8] M. Deuring, Imaginäre quadratische Zahlkörper mit der Klassenzahl Eins, Invent. Math. 5 (1968), 169-179. | Zbl 0155.38001

[008] [9] C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966.

[009] [10] D. M. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa 3 (1976), 623-663. | Zbl 0345.12007

[010] [11] B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87.

[011] [12] G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, London, 1968. | Zbl 0020.29201

[012] [13] K. Heegner, Diophantische Analysis und Modulfunktionen, Math. Z. 56 (1952), 227-253. | Zbl 0049.16202

[013] [14] H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford Ser. 25 (1934), 150-160. | Zbl 0009.29602

[014] [15] A. E. Ingham, The Distribution of Prime Numbers, Cambridge Tracts in Math. 30, Cambridge Univ. Press, Cambridge, 1990.

[015] [16] H. Kestelman, Modern Theories of Integration, Dover, New York, 1960.

[016] [17] N. Levinson and R. M. Redheffer, Complex Variables, Holden-Day, San Francisco, 1970. | Zbl 0201.40202

[017] [18] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542. | Zbl 0285.12004

[018] [19] J. Oesterlé, Nombres de classes des corps quadratiques imaginaires, Sém. Bourbaki, 1983-1984, exp. 631.

[019] [20] C. L. Siegel, Über die Classenzahl quadratischer Zahlkörper, Acta Arith. 1 (1936), 83-86. | Zbl 61.0170.02

[020] [21] C. L. Siegel, Zum Beweise des Starkschen Satzes, Invent. Math. 5 (1968), 180-191. | Zbl 0175.33602

[021] [22] H. M. Stark, On complex quadratic number fields with class number equal to one, Trans. Amer. Math. Soc. 122 (1966), 112-119. | Zbl 0137.02401

[022] [23] H. M. Stark, A complete determination of the complex quadratic fields of class number one, Michigan Math. J. 14 (1967), 1-27.

[023] [24] H. M. Stark, On the 'gap' in a theorem of Heegner, J. Number Theory 1 (1969), 16-27. | Zbl 0198.37702

[024] [25] H. M. Stark, L-functions and character sums for quadratic forms (II), Acta Arith. 15 (1969), 307-317.

[025] [26] H. M. Stark, A transcendence theorem for class number problems, Ann. of Math. 94 (1971), 153-173. | Zbl 0229.12010

[026] [27] H. M. Stark, On a transcendence theorem for class number problems II, Ann. of Math. 96 (1972), 251-259.

[027] [28] H. M. Stark, On complex quadratic fields with class number two, Math. Comp. 29 (1975), 289-302. | Zbl 0321.12009

[028] [29] G. N. Watson, A Treatise on the Theory of Bessel Functions, 2nd ed., Cambridge Univ. Press, London, 1966. | Zbl 0174.36202

[029] [30] A. Weil, On some exponential sums, Proc. Nat. Acad. Sci. U.S.A. 34 (1948), 204-220. | Zbl 0032.26102

[030] [31] P. J. Weinberger, On small zeros of Dirichlet L-functions, Math. Comp. 29 (1975), 319-328. | Zbl 0301.10035