PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
1997 | 80 | 3 | 249-272
Tytuł artykułu

4-core partitions and class numbers

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Czasopismo
Rocznik
Tom
80
Numer
3
Strony
249-272
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-09-26
Twórcy
autor
  • School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.
autor
  • Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802, U.S.A.
Bibliografia
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-aav80i3p249bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.