Exceptional modular form of weight 4 on an exceptional domain contained in C27.

Título inglés Exceptional modular form of weight 4 on an exceptional domain contained in C27.
Título español Forma modular excepcional de peso 4 sobre un dominio excepcional contenido en C27.
Autor/es Kim, Henry H.
Organización Dep. Math. Univ. Chicago, Chicago (Illinois), Estados Unidos
Revista 0213-2230
Publicación 1993, 9 (1): 139-200, 16 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés Resnikoff [12] proved that weights of a non trivial singular modular form should be integral multiples of 1/2, 1, 2, 4 for the Siegel, Hermitian, quaternion and exceptional cases, respectively. The θ-functions in the Siegel, Hermitian and quaternion cases provide examples of singular modular forms (Krieg [10]). Shimura [15] obtained a modular form of half-integral weight by analytically continuing an Eisenstein series. Bump and Bailey suggested the possibility of applying an analogue of Shimura's method to obtain singular modular forms, i.e. modular forms of weight 4 and 8, on the exceptional domain of 3 x 3 hermitian matrices over Cayley numbers. The idea is to use Fourier expansion of a non-holomorphic Eisenstein series defined by using the factor of automorphy as in Karel [7]. The Fourier coefficients are the product of confluent hypergeometric functions as in Nagaoka [11] and certain singular series which we calculate by the method of Karel [6]. In this note we describe a modular form of weight 4 which may be viewed as an analogue of a θ zero-value and as an application, we consider its Mellin transform and prove a functional equation of the Eisenstein series which is a Nagaoka's conjecture (Nagaoka [11]).
Clasificación UNESCO 120501
Palabras clave español Formas modulares ; Teoría de formas automórficas ; Series de Eisenstein ; Expansión ; Análisis de Fourier
Código MathReviews MR1216126
Código Z-Math Zbl 0777.11015
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