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)-ktÎo 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-4p 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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