4-core partitions and class numbers

• Autorzy: Ken Ono , Lawrence Sze
• Języki publikacji: EN

Słowa kluczowe

EN

4-core partitions; class numbers

Kategorie tematyczne

• 11P99: None of the above, but in this section
• 20C20: Modular representations and characters

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 80
• Numer: 3
• Strony: 249-272

Daty

wydano

1997

otrzymano

1996-09-26

Twórcy

autor

Ken Ono

• School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540, U.S.A.

autor

Lawrence Sze

• 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.