Fourier coefficients of Jacobi forms over Cayley numbers.

Título inglés	Fourier coefficients of Jacobi forms over Cayley numbers.
Título español	Coeficientes de Fourier de formas de Jacobi sobre números de Cayley.
Autor/es	Eie, Min King
Organización	Inst. Math. Acad. Sinica, Nankang (Taipei), Taiwan;Inst. Appl. Math. Natl. Chung Cheng Univ., Ming-Hsiung (Chia-Yi), Taiwan
Revista	0213-2230
Publicación	1995, 11 (1): 125-142, 7 Ref.
Tipo de documento	articulo
Idioma	Inglés
Resumen inglés	In this paper we shall compute explicitly the Fourier coefficients of the Eisenstein series Ek,m(z,w) = 1/2 ∑(c,d)=1 (cz + d)-k ∑tÎo exp {2πim((az + b/cz +d)N(t)) + σ(t,(w/cz +d) - (cN(w)/cz + d)} which is a Jacobi form of weight k and index m defined on H1 x CC, the product of the upper half-plane and Cayley numbers over the complex field C. The coefficient of e2πi(nz + σ(t,w)) with nm > N(t) has the form -2(k - 4)/Bk-4 ∏p Sp Here Sp is an elementary factor which depends only on νp(m), νp(t), νp(n) and νp(nm - N(t)) = 0. Also Sp = 1 for almost all p. Indeed, one has Sp = 1 if νp(m) = νp(nm - N(t)) = 0. An explicit formula for Sp will be given in details. In particular, these Fourier coefficients are rational numbers.
Clasificación UNESCO	120212
Palabras clave español	Series de Eisenstein ; Series de Fourier ; Coeficientes
Código MathReviews	MR1321775
Código Z-Math	Zbl 0824.11032
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