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ArticleOriginal scientific text

Title

4-core partitions and class numbers

Authors 1, 2

Affiliations

  1. School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.
  2. Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.

Keywords

ENG
4-core partitions, class numbers

Bibliography

  1. G. Andrews, The Theory of Partitions, Addison-Wesley, 1976.
  2. G. Andrews, C. Bessenrodt and J. Olsson, Partition identities and labels for some modular characters, Trans. Amer. Math. Soc. 344 (1994), 597-615.
  3. G. Andrews and F. Garvan, Dyson's crank of a partition, Bull. Amer. Math. Soc. 18 (1988), 167-171.
  4. A. O. L. Atkin and P. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. (3) 4 (1954), 84-106.
  5. Z. Borevich and I. Shafarevich, Number Theory, Academic Press, New York, 1966.
  6. R. Brauer, Representations of Finite Simple Groups, Lecture Notes on Modern Math. 1, Wiley, New York, 1963, 133-175.
  7. H. Cohen and H. Lenstra, Heuristics on class groups of number fields, in: Lecture Notes in Math. 1068, Springer, New York, 1984, 33-61.
  8. D. Cox, Primes of the Form x² + ny², Wiley, New York, 1989.
  9. F. Dyson, Some guesses in the theory of partitions, Eureka (Cambridge) 8 (1944), 10-15.
  10. K. Erdmann and G. Michler, Blocks for symmetric groups and their covering groups and quadratic forms, Beitr. Algebra Geom. 37 (1996), 103-118.
  11. P. Fong and B. Srinivasan, The blocks of finite general linear groups and unitary groups, Invent. Math. 69 (1982), 109-153.
  12. F. Garvan, Some congruence properties for partitions that are p-cores, Proc. London Math. Soc. 66 (1993), 449-478.
  13. F. Garvan, D. Kim and D. Stanton, Cranks and t-cores, Invent. Math. 101 (1990), 1-17.
  14. C. F. Gauss, Disquisitiones Arithmeticae, transl. A. A. Clarke, Yale Univ. Press, 1966.
  15. D. Goldfeld, The class number of quadratic fields and the Birch and Swinnerton-Dyer Conjecture, Ann. Scuola Norm. Sup. Pisa 3 (1976), 623-663.
  16. A. Granville and K. Ono, Defect zero p-blocks for finite simple groups, Trans. Amer. Math. Soc. 348 (1996), 331-347.
  17. B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87.
  18. M. Hirschhorn and J. Sellers, Some amazing facts about 4-cores, J. Number Theory 60 (1996), 51-69.
  19. M. Hirschhorn and J. Sellers, Two congruences involving 4-cores, Electron. J. Combin. 3 (2) (1996).
  20. M. Isaacs, Character Theory of Finite Simple Groups, Academic Press, New York, 1976.
  21. G. James and A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, 1979.
  22. B. Jones, The Arithmetic Theory of Quadratic Forms, Carus Math. Monographs 10, Math. Assoc. Amer., Wiley, 1950.
  23. I. Kiming, A note on a theorem of A. Granville and K. Ono, J. Number Theory 60 (1996), 97-102.
  24. I. Kiming, On the number of p-spin blocks of defect zero of covering groups of symmetric groups, preprint.
  25. A. Klyachko, Modular forms and representations of symmetric groups, integral lattices and finite linear groups, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 116 (1982), 74-85 (in Russian).
  26. N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, New York, 1984.
  27. J. Oesterlé, Nombre de classes des corps quadratiques imaginaires, Sém. Bourbaki, Astérisque 121-122 (1985), 309-323.
  28. J. Olsson, Combinatorics and representations of finite groups, Univ. Essen Lect. Notes 20, 1993.
  29. K. Ono, On the positivity of the number of t-core partitions, Acta Arith. 66 (1994), 221-228.
  30. K. Ono, A note on the number of t-core partitions, Rocky Mountain J. Math. 25 (1995), 1165-1169.
  31. K. Ono, Rank zero quadratic twists of modular elliptic curves, Compositio Math. 104 (1996), 293-304.
  32. K. Ono, Twists of elliptic curves, Compositio Math. to appear.
  33. G. de Robinson, Representation Theory of the Symmetric Group, Toronto Univ. Press, 1961.
  34. G. Shimura, On modular forms of half-integral weight, Ann. of Math. 97 (1973), 440-481.
  35. J. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986.
  36. J.-L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375-484.
Acta Arithmetica
1997/80/3
Export to PBN, Opens in new tab
Pages:
249-272
Main language of publication
English
Received
1996-09-26
Published
1997
Exact and natural sciences