Resumen de Fourier coefficients of Jacobi forms over Cayley numbers
Minking Eie
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 {2pim((az + b/cz +d)N(t)) + s(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 e2pi(nz + s(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 ?p(m), ?p(t), ?p(n) and ?p(nm - N(t)) = 0. Also Sp = 1 for almost all p. Indeed, one has Sp = 1 if ?p(m) = ?p(nm - N(t)) = 0. An explicit formula for Sp will be given in details. In particular, these Fourier coefficients are rational numbers.
