Congruences for Certain Theta Series

Journal of Number Theory

Volumn 71, Issue 1, 1998, Pages 86-105

  Dummigan, Neil ^a   Tiep, Pham Huu ^b,c  

^a NORTHERN ILLINOIS UNIVERSITY   (United States)

^b OHIO STATE UNIVERSITY   (United States)

^c UNIVERSITY OF FLORIDA   (United States)

Author keywords

Even unimodular lattice; Mordell Weil lattice; Theta series; Weil representation

Indexed keywords

EID: 0002792164     PISSN: 0022314X     EISSN: None     Source Type: Journal    
DOI: 10.1006/jnth.1998.2234     Document Type: Article

References (39)

1. Conway J. H., Norton S. P., Parker R. A., Wilson R. A. An ATLAS of finite groups. 1985;Clarendon Press, Oxford.
2. Bayer-Fluckiger E. Definite unimodular lattices having an automorphism of given characteristic polynomial. Comment. Math. Helv. 54:1984;509-538.
3. Bayer-Fluckiger E. Réseaux unimodulaires. Sém. Théorie Nombres Bordeaux. 1:1989;189-196.
4. Bayer-Fluckiger E. Lattices with automorphisms of given characteristic polynomial. Prépublications de L'équipe de Mathématiques de Besancon. 1996.
5. Broué M., Enguehard M. Une famille infinie de formes quadratiques entières; leurs groupes d'automorphismes. Ann. Sci. École Norm. Sup. 6:1973;17-52.
6. Barnes E. S., Wall G. E. Some extreme forms defined in terms of abelian groups. J. Austral. Math. Soc. 1:1959;47-63.
7. Conway J. H., Sloane N. J. A. Sphere packings, lattices and groups. Grundlehren Math. Wiss. 290:1988;Springer-Verlag, Berlin and New York.
8. Dummigan N. Algebraic cycles and even unimodular lattices. J. London Math. Soc. (2). 56:1997;209-221.
9. Dummigan N. Symplectic group lattices as Mordell-Weil sublattices. J. Number Theory. 61:1996;365-387.
10. N. Dummigan, Pham, Huu, Tiep, Lower bounds for certain symplectic group and unitary group lattices.
11. Elkies N. D. Mordell-Weil lattices in characteristic 2: I. Construction and first properties. Int. Math. Res. Notices. 8:1994;343-360.
12. Fleischmann P., Lempken W., Tiep Pham Huu. Finitep. J. Algebra. 188:1997;547-579.
13. Gérardin P. Weil representations associated to finite fields. J. Algebra. 46:1977;54-101.
14. Gorenstein D. Finite Groups. 1968;Harper and Row, New York.
15. Gouvêa F. Q. Arithmetic ofp. Lecture Notes in Math. 1304:1988;Springer-Verlag, Berlin and New York.
16. Gow R. Even unimodular lattices associated with the Weil representation of the finite symplectic group. J. Algebra. 122:1989;510-519.
17. Gross B. H. Group representations and lattices. J. Amer. Math. Soc. 3:1990;929-960.
18. Hartsthorne R. Algebraic Geometry. 1977;Springer-Verlag, New York.
19. Hotta R., Matsui K. On a lemma of Tate-Thompson. Hiroshima Math. J. 8:1978;255-2668.
20. Kleidman P. B., Liebeck M. W. The Subgroup Structure of the finite Classical Groups. London Math. Soc. Lecture Note Ser. No. 129. 1990;Cambridge University Press.
21. Katsura T., Shioda T. On Fermat varieties. Tohoku Math. J. 31:1979;97-115.
22. Katz N. p. Modular functions of one variable III. Lecture Notes in Math. 350:1973;Springer-Verlag, Berlin and New York.
23. Landazuri V., Seitz G. On the minimal degrees of projective representations of finite Chevalley groups. J. Algebra. 32:1974;418-443.
24. Milne J. S. The Tate-Shafarevich group of a constant abelian variety. Invent. Math. 6:1968;91-105.
25. Ogg A. Modular Forms and Dirichlet Series. 1969;Benjamin, New York.
26. Quebbemann H.-G. Unimodular lattices with isometries of large prime order II. Math. Nachr. 156:1992;219-224.
27. Reifart A. A characterization of Thompson's sporadic simple group. J. Algebra. 38:1976;192-200.
28. Schoeneberg B. Elliptic modular functions. Grundlehren Math. Wiss. 203:1974;Springer-Verlag, Berlin.
29. Serre J.-P. Formes modulaires et functions zêtap. Modular functions of one variable III. Lecture Notes in Math. 350:1973;Springer-Verlag, Berlin and New York.
30. Serre J.-P. A Course in Arithmetic. GTM. 7:1973;Springer-Verlag, New York.
31. Shioda T. Mordell-Weil lattices and sphere-packings. Amer. Jour. Math. 113:1991;931-948.
32. Swinnerton-Dyer H. P. F. Onl. Modular functions of one variable III. Lecture Notes in Math. 350:1973;Springer-Verlag, Berlin and New York.
33. Tate J. Endomorphisms of abelian varieties over finite fields. Invent. Math. 2:1966;134-144.
34. Tate J. Algebraic cycles and poles of zeta functions. Schilling O. F. G. Arithmetical Algebraic Geometry. 1965;93-110 Harper and Row, New York.
35. 8. Iwahori N. Finite Groups Symposium. 1976;113-116.
36. Tiep Pham Huu. Globally irreducible representations of finite groups and integral lattices. Geometriae Dedicata. 64:1997;85-123.
37. Tiep Pham Huu. Weil representations as globally irreducible representations. Math. Nachr. 184:1997;313-327.
38. Tiep Pham Huu, Zalesskii A. E. Minimal characters of the finite classical groups. Comm. Algebra. 24:1996;2093-2167.
39. Washington L. C. Introduction to Cyclotomic Fields. 1982;Springer-Verlag, New York.