Fumitake Hyodo
Published 2021-10-05, updated 2022-02-17Version 2
This study concerns (not necessarily commutative) Hecke rings associated with certain algebras and describes a formal Dirichlet series with coefficients in the Hecke rings, which can be used to generalize Shimura's series. Considering the case of Heisenberg Lie algebra, an analog of the identity for Shimura's series derived employing the rationality theorem, presented by Hecke and Tamagawa, is established.
A note on a Hecke ring associated with the Heisenberg Lie algebra
A formal power series over a noncommutative Hecke ring and the rationality of the Hecke series for $GSp_4$
Algebra of formal power series, isomorphic to the algebra of formal Dirichlet series
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