@article{bwmeta1.element.bwnjournal-article-aav80i3p249bwm,
author = {Ken Ono and Lawrence Sze},
title = {4-core partitions and class numbers},
journal = {Acta Arithmetica},
volume = {80},
year = {1997},
pages = {249-272},
zbl = {0868.11047},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav80i3p249bwm}
}
Ken Ono; Lawrence Sze. 4-core partitions and class numbers. Acta Arithmetica, Tome 80 (1997) pp. 249-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav80i3p249bwm/
[000] [1] G. Andrews, The Theory of Partitions, Addison-Wesley, 1976. | Zbl 0371.10001
[001] [2] G. Andrews, C. Bessenrodt and J. Olsson, Partition identities and labels for some modular characters, Trans. Amer. Math. Soc. 344 (1994), 597-615. | Zbl 0806.05065
[002] [3] G. Andrews and F. Garvan, Dyson's crank of a partition, Bull. Amer. Math. Soc. 18 (1988), 167-171. | Zbl 0646.10008
[003] [4] A. O. L. Atkin and P. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. (3) 4 (1954), 84-106. | Zbl 0055.03805
[004] [5] Z. Borevich and I. Shafarevich, Number Theory, Academic Press, New York, 1966.
[005] [6] R. Brauer, Representations of Finite Simple Groups, Lecture Notes on Modern Math. 1, Wiley, New York, 1963, 133-175.
[006] [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.
[007] [8] D. Cox, Primes of the Form x² + ny², Wiley, New York, 1989.
[008] [9] F. Dyson, Some guesses in the theory of partitions, Eureka (Cambridge) 8 (1944), 10-15.
[009] [10] K. Erdmann and G. Michler, Blocks for symmetric groups and their covering groups and quadratic forms, Beitr. Algebra Geom. 37 (1996), 103-118. | Zbl 0894.20014
[010] [11] P. Fong and B. Srinivasan, The blocks of finite general linear groups and unitary groups, Invent. Math. 69 (1982), 109-153. | Zbl 0507.20007
[011] [12] F. Garvan, Some congruence properties for partitions that are p-cores, Proc. London Math. Soc. 66 (1993), 449-478. | Zbl 0788.11044
[012] [13] F. Garvan, D. Kim and D. Stanton, Cranks and t-cores, Invent. Math. 101 (1990), 1-17. | Zbl 0721.11039
[013] [14] C. F. Gauss, Disquisitiones Arithmeticae, transl. A. A. Clarke, Yale Univ. Press, 1966.
[014] [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. | Zbl 0345.12007
[015] [16] A. Granville and K. Ono, Defect zero p-blocks for finite simple groups, Trans. Amer. Math. Soc. 348 (1996), 331-347. | Zbl 0855.20007
[016] [17] B. Gross et D. Zagier, Points de Heegner et derivées de fonctions L, C. R. Acad. Sci. Paris 297 (1983), 85-87.
[017] [18] M. Hirschhorn and J. Sellers, Some amazing facts about 4-cores, J. Number Theory 60 (1996), 51-69. | Zbl 0864.11050
[018] [19] M. Hirschhorn and J. Sellers, Two congruences involving 4-cores, Electron. J. Combin. 3 (2) (1996). | Zbl 0857.05009
[019] [20] M. Isaacs, Character Theory of Finite Simple Groups, Academic Press, New York, 1976.
[020] [21] G. James and A. Kerber, The Representation Theory of the Symmetric Group, Addison-Wesley, Reading, 1979.
[021] [22] B. Jones, The Arithmetic Theory of Quadratic Forms, Carus Math. Monographs 10, Math. Assoc. Amer., Wiley, 1950.
[022] [23] I. Kiming, A note on a theorem of A. Granville and K. Ono, J. Number Theory 60 (1996), 97-102.
[023] [24] I. Kiming, On the number of p-spin blocks of defect zero of covering groups of symmetric groups, preprint.
[024] [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). | Zbl 0512.10019
[025] [26] N. Koblitz, Introduction to Elliptic Curves and Modular Forms, Springer, New York, 1984. | Zbl 0553.10019
[026] [27] J. Oesterlé, Nombre de classes des corps quadratiques imaginaires, Sém. Bourbaki, Astérisque 121-122 (1985), 309-323.
[027] [28] J. Olsson, Combinatorics and representations of finite groups, Univ. Essen Lect. Notes 20, 1993. | Zbl 0796.05095
[028] [29] K. Ono, On the positivity of the number of t-core partitions, Acta Arith. 66 (1994), 221-228. | Zbl 0793.11027
[029] [30] K. Ono, A note on the number of t-core partitions, Rocky Mountain J. Math. 25 (1995), 1165-1169. | Zbl 0852.11055
[030] [31] K. Ono, Rank zero quadratic twists of modular elliptic curves, Compositio Math. 104 (1996), 293-304. | Zbl 0876.11025
[031] [32] K. Ono, Twists of elliptic curves, Compositio Math. to appear.
[032] [33] G. de Robinson, Representation Theory of the Symmetric Group, Toronto Univ. Press, 1961. | Zbl 0102.02002
[033] [34] G. Shimura, On modular forms of half-integral weight, Ann. of Math. 97 (1973), 440-481. | Zbl 0266.10022
[034] [35] J. Silverman, The Arithmetic of Elliptic Curves, Springer, New York, 1986. | Zbl 0585.14026
[035] [36] J.-L. Waldspurger, Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pures Appl. 60 (1981), 375-484. | Zbl 0431.10015