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We prove the existence of meromorphic continuation and the functional equation of the real analytic Jacobi Eisenstein series of degree m and matrix index T in case T is a kernel form. Keywords Siegel modular forms · Jacobi forms · Eisenstein series Mathematics Subject Classification 11F46 · 11F50 1 Introduction For m, l ∈ Z let >0 G := Sp (R) H (R) m,l 2m m,l be the Jacobi group, where H (R) is the Heisenberg group. Let H be the Siegel upper m,l m (l,m) J half space of degree m and C the set of complex l × m matrices. The group G acts m,l (l,m) on H × C in a natural way. Let J J := Sp (Z) and := G (Z). 2m m,l m,l (l,m) (l,m) (l) For a ∈ C we write a = a and a = a if l = m. The transpose of a is denoted by a.Let A be the set of symmetric positive definite semi-integral matrices of size l. (l,m) For k ∈ 2Z , T ∈ A , and a variable (z,w) on H × C , the real analytic Jacobi ≥0 m Eisenstein series
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Jan 14, 2019
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