Abstract
In this paper, we focus on solvable prehomogeneous vector spaces associated with homogeneous cones, and consider the associated zeta functions in several variables. We discuss $\mathbb{Q}$-structures of these prehomogeneous vector spaces, and give explicit formulas of functional equations of the zeta functions by using the data of homogeneous cones. The associated $b$-functions are also described explicitly.
Citation
Hideto Nakashima. "Functional equations of zeta functions associated with homogeneous cones." Tohoku Math. J. (2) 72 (3) 349 - 378, 2020. https://doi.org/10.2748/tmj/1601085620
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