The imaginary quadratic fields of class number 4

Steven Arno

Acta Arithmetica (1992)

  • Volume: 60, Issue: 4, page 321-334
  • ISSN: 0065-1036

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Steven Arno. "The imaginary quadratic fields of class number 4." Acta Arithmetica 60.4 (1992): 321-334. <http://eudml.org/doc/206441>.

@article{StevenArno1992,
author = {Steven Arno},
journal = {Acta Arithmetica},
keywords = {imaginary quadratic fields; class number 4; sum of three squares},
language = {eng},
number = {4},
pages = {321-334},
title = {The imaginary quadratic fields of class number 4},
url = {http://eudml.org/doc/206441},
volume = {60},
year = {1992},
}

TY - JOUR
AU - Steven Arno
TI - The imaginary quadratic fields of class number 4
JO - Acta Arithmetica
PY - 1992
VL - 60
IS - 4
SP - 321
EP - 334
LA - eng
KW - imaginary quadratic fields; class number 4; sum of three squares
UR - http://eudml.org/doc/206441
ER -

References

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  1. [1] N. C. Ankeny, The least quadratic non residue, Ann. of Math. (2) 55 (1952), 65-72. Zbl0046.04006
  2. [2] A. Baker, A remark on the class number of quadratic fields, Bull. London Math. Soc. 1 (1966), 98-102. 
  3. [3] A. Baker, Imaginary quadratic fields of class number 2, Ann. of Math. 94 (1971), 139-152. 
  4. [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. Zbl0558.10038
  5. [5] Z. I. Borevich and I. R. Shafarevich, Number Theory, Academic Press, New York 1966. 
  6. [6] D. A. Buell, Small class numbers and extreme values of L-functions of quadratic fields, Math. Comp. 31 (1977), 786-796. Zbl0379.12001
  7. [7] P. Chowla and A. Selberg, On Epstein's zeta function, J. Reine Angew. Math. 227 (1967), 86-110. Zbl0166.05204
  8. [8] H. Davenport, Multiplicative Number Theory, 2nd ed., Graduate Texts in Math. 74, Springer, New York 1980. Zbl0453.10002
  9. [9] C. B. Haselgrove and J. C. P. Miller, Tables of the Riemann Zeta Function, Royal Society Math. Tables, Vol. 6, Cambridge 1960. Zbl0095.12001
  10. [10] H. Heilbronn, On the class number in imaginary quadratic fields, Quart. J. Math. Oxford Ser. 25 (1934), 150-160. Zbl0009.29602
  11. [11] C. F. Gauss, Disquisitiones Arithmeticae, Yale Univ. Press, 1966. 
  12. [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. Zbl0345.12007
  13. [13] B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87. 
  14. [14] D. H. Lehmer, E. Lehmer, and D. Shanks, Integer sequences having prescribed quadratic character, Math. Comp. 24 (1970), 433-451. Zbl0203.35301
  15. [15] H. L. Montgomery and P. J. Weinberger, Notes on small class numbers, Acta Arith. 24 (1974), 529-542. Zbl0285.12004
  16. [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. [17] J. Oesterlé, Nombres de classes des corps quadratiques imaginaires, Sém. Bourbaki, 1983-1984, exp. 631. 
  18. [18] H. M. Stark, A complete determination of the complex quadratic fields of class number 1, Michigan Math. J. 14 (1967), 1-27. Zbl0148.27802
  19. [19] H. M. Stark, On complex quadratic fields with class number two, Math. Comp. 29 (1975), 289-302. Zbl0321.12009
  20. [20] H. M. Stark, L-functions and character sums for quadratic forms (II), Acta Arith. 15 (1969), 307-317. 
  21. [21] E. C. Titchmarsh, The Theory of the Riemann Zeta-Function, Oxford Univ. Press, London 1951. Zbl0042.07901

Citations in EuDML Documents

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  1. R. A. Mollin, Quadratic polynomials producing consecutive, distinct primes and class groups of complex quadratic fields
  2. Ku-Young Chang, Soun-Hi Kwon, The imaginary abelian number fields with class numbers equal to their genus class numbers
  3. Steven Arno, M. L. Robinson, Ferrell S. Wheeler, Imaginary quadratic fields with small odd class number
  4. Young-Ho Park, Soun-Hi Kwon, Determination of all imaginary abelian sextic number fields with class number ≤ 11
  5. Joseph B. Muskat, Blair K. Spearman, Kenneth S. Williams, Predictive criteria for the representation of primes by binary quadratic forms
  6. Ken Yamamura, Maximal unramified extensions of imaginary quadratic number fields of small conductors
  7. Ken Yamamura, Determination of the imaginary normal octic number fields with class number one which are not CM-fields
  8. Ryotaro Okazaki, Inclusion of CM-fields and divisibility ofrelative class numbers

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