Year: 2026
Type: article
Abstract: We investigate the analytic properties of a Dirichlet series involving the Fourier–Jacobi coefficients of two cusp forms for orthogonal groups of signature $$(2,n+2)$$ ( 2 , n + 2 ) . Using an orthogonal Eisenstein series of Klingen type, we obtain an integral representation for this Dirichlet series. In the case when the corresponding lattice has only one 1-dimensional cusp, we rewrite this Eisenstein series in the form of an Epstein zeta function. If additionally $$4 \mid n$$ 4 ∣ n , we deduce a theta correspondence between this Eisenstein series and a Siegel Eisenstein series for the symplectic group of degree 2. We obtain, in this way, the meromorphic continuation of the Dirichlet series to $$\mathbb {C}$$ C as a corollary. In the case of the $$E_8$$ E 8 lattice, we are able to further deduce a precise functional equation for the Dirichlet series.
Source: The Ramanujan Journal
Author: Rafail Psyroukis
Institution: Durham University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,990
OpenAlex ID: W7141864419