Zeta functions over \(\mathbb F_1\)

DOI10.3792/pjaa.81.180zbMath1141.11316OpenAlexW2003023727MaRDI QIDQ935668

Nobushige Kurokawa

Publication date: 12 August 2008

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.81.180

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Finite ground fields in algebraic geometry (14G15) Varieties over finite and local fields (11G25) Zeta functions and (L)-functions (11S40) (K)-theory of local fields (11S70)

Related Items (16)

The Riemann hypothesis and functional equations for zeta functions over \(\mathbb F_1\) ⋮ Deitmar schemes, graphs and zeta functions ⋮ Absolute zeta functions ⋮ A \(p\)-analogue of Euler's constant and congruence zeta functions ⋮ Remarks on zeta functions and \(K\)-theory over \({\mathbb F}_1\) ⋮ Functional equations for zeta functions of \(\mathbb F_1\)-schemes ⋮ Towards the horizons of Tits's vision: on band schemes, crowds and \(\mathbb{F}_1\)-structures ⋮ Torified varieties and their geometries over \(\mathbb{F}_{1}\) ⋮ Absolute zeta functions and absolute automorphic forms ⋮ Representation theory over tropical semifield and Langlands duality ⋮ Dualities for absolute zeta functions and multiple gamma functions ⋮ The structure of Deitmar schemes. I. ⋮ Values of absolute tensor products ⋮ Zeta functions of certain noncommutative algebras ⋮ An arithmetic site at the complex place ⋮ Linear recursive sequences andSpec(ℤ) over𝔽₁

Cites Work

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• Values of absolute tensor products
• Absolute derivations and zeta functions
• A prime geodesic theorem for higher rank spaces
• Absolute Frobenius operators
• Zeta functions and normalized multiple sine functions
• On the groups \(J(X)\). IV
• The Adams conjecture
• On the cohomology and K-theory of the general linear groups over a finite field
• The notion of dimension in geometry and algebra

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