Glasnik Matematicki, Vol. 60, No. 2 (2025), 197-206. \( \)

DEGENERATE EISENSTEIN SERIES ON THE SYMPLECTIC GROUP OF RANK TWO REVISITED BY A NEW METHOD FOR PROVING HOLOMORPHY

Neven Grbac

Juraj Dobrila University of Pula, 52100 Pula, Croatia
e-mail:neven.grbac@unipu.hr

Abstract.   In a recent preprint entitled “Holomorphy of Eisenstein series – a new method and applications in the case of the general linear group”, the author has developed a new method for proving holomorphy of degenerate Eisenstein series, based on the Franke filtration of spaces of automorphic forms. In this paper, the method is applied in the case of degenerate Eisenstein series on the symplectic group of rank two. Although the analytic properties of Eisenstein series in that case are already known, the goal is to exhibit the method in a simple setting, in which all additional technical details are peeled off.

2020 Mathematics Subject Classification.   11F70, 22E55

Key words and phrases.   Eisenstein series, Franke filtration, method for proving holomorphy, symplectic group of rank two

https://doi.org/10.3336/gm.60.2.02

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