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The Riemann hypothesis and functional equations for zeta functions over \(\mathbb F_1\). (English) Zbl 1275.11125

Summary: We prove functional equations for the absolute zeta functions. We also show that the absolute zeta functions satisfy the tensor structure in the sense that their singularities possess an additive property under the tensor product. Moreover those singularities satisfy the analog of the Riemann hypothesis.

MSC:

11M38 Zeta and \(L\)-functions in characteristic \(p\)
14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
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References:

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