# Fourier coefficients of Jacobi forms over Cayley numbers.

Revista Matemática Iberoamericana (1995)

- Volume: 11, Issue: 1, page 125-142
- ISSN: 0213-2230

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topEie, Min King. "Fourier coefficients of Jacobi forms over Cayley numbers.." Revista Matemática Iberoamericana 11.1 (1995): 125-142. <http://eudml.org/doc/39482>.

@article{Eie1995,

abstract = {In this paper we shall compute explicitly the Fourier coefficients of the Eisenstein seriesEk,m(z,w) = 1/2 ∑(c,d)=1 (cz + d)-k ∑t∈o 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 SpHere 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.},

author = {Eie, Min King},

journal = {Revista Matemática Iberoamericana},

keywords = {Series de Eisenstein; Series de Fourier; Coeficientes; Jacobi forms; Cayley numbers; Eisenstein series; Fourier coefficients},

language = {eng},

number = {1},

pages = {125-142},

title = {Fourier coefficients of Jacobi forms over Cayley numbers.},

url = {http://eudml.org/doc/39482},

volume = {11},

year = {1995},

}

TY - JOUR

AU - Eie, Min King

TI - Fourier coefficients of Jacobi forms over Cayley numbers.

JO - Revista Matemática Iberoamericana

PY - 1995

VL - 11

IS - 1

SP - 125

EP - 142

AB - In this paper we shall compute explicitly the Fourier coefficients of the Eisenstein seriesEk,m(z,w) = 1/2 ∑(c,d)=1 (cz + d)-k ∑t∈o 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 SpHere 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.

LA - eng

KW - Series de Eisenstein; Series de Fourier; Coeficientes; Jacobi forms; Cayley numbers; Eisenstein series; Fourier coefficients

UR - http://eudml.org/doc/39482

ER -

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