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Title

The imaginary quadratic fields of class number 4

Authors 1

Affiliations

  1. The Supercomputing Research Center, 17100 Science Drive, Bowie, Maryland 20715, U.S.A.

Bibliography

  1. N. C. Ankeny, The least quadratic non residue, Ann. of Math. (2) 55 (1952), 65-72.
  2. A. Baker, A remark on the class number of quadratic fields, Bull. London Math. Soc. 1 (1966), 98-102.
  3. A. Baker, Imaginary quadratic fields of class number 2, Ann. of Math. 94 (1971), 139-152.
  4. P. T. Bateman and E. Grosswald, Positive integers expressible as a sum of 3 squares in essentially only one way, J. Number Theory 19 (1984), 301-308.
  5. Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York 1966.
  6. D. A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp. 31 (1977), 786-796.
  7. P. Chowla and A. Selberg, On Epstein's zeta function, J. Reine Angew. Math. 227 (1967), 86-110.
  8. H. Davenport, Multiplicative Number Theory, 2nd ed., Graduate Texts in Math. 74, Springer, New York 1980.
  9. C. B. Haselgrove and J. C. P. Miller, Tables of the Riemann Zeta Function, Royal Society Math. Tables, Vol. 6, Cambridge 1960.
  10. H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford Ser. 25 (1934), 150-160.
  11. C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966.
  12. D. M. Goldfeld, The class number of quadratic fields and the conjectures of Birch and Swinnerton-Dyer, Ann. Scuola Norm. Sup. Pisa (4) 3 (1976), 623-663.
  13. B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87.
  14. D. H. Lehmer, E. Lehmer, and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp. 24 (1970), 433-451.
  15. H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542.
  16. L. J. Mordell, On the rational solutions of the indeterminate equations of the 3rd and 4rth degrees, Proc. Cambridge Philos. Soc. 21 (1922), 179-192.
  17. J. Oesterlé, Nombres de classes des corps quadratiques imaginaires, Sém. Bourbaki, 1983-1984, exp. 631.
  18. H. M. Stark, A complete determination of the complex quadratic fields of class number 1, Michigan Math. J. 14 (1967), 1-27.
  19. H. M. Stark, On complex quadratic fields with class number two, Math. Comp. 29 (1975), 289-302.
  20. H. M. Stark, L-functions and character sums for quadratic forms (II), Acta Arith. 15 (1969), 307-317.
  21. E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, London 1951.
Acta Arithmetica
1991-1992/60/4
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Pages:
321-334
Main language of publication
English
Received
1990-08-17
Accepted
1991-03-26
Published
1992
Exact and natural sciences