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Functional equations for Selberg zeta functions with Tate motives

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For a compact Riemann surface $M$ of genus $g\ge 2$, we study the functional equations of the Selberg zeta functions attached with the Tate motives $f$. We prove that certain… Click to show full abstract

For a compact Riemann surface $M$ of genus $g\ge 2$, we study the functional equations of the Selberg zeta functions attached with the Tate motives $f$. We prove that certain functional equations hold if and only if $f$ has the absolute automorphy.

Keywords: zeta functions; equations selberg; functions tate; selberg zeta; tate motives; functional equations

Journal Title: Journal of Number Theory
Year Published: 2021

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