Height zeta functions of projective bundles

2015/11/30 by Takuya Maruyama, Maruyama, Takuya
Mathematics · #14G40 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic and geometric function theory #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:14G40

paper · pdf · doi:10.48550/arxiv.1511.09266

19 pages

arxiv created 2015/11/30 · openalex publication_date 2015/11/30 · arxiv updated 2015/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new approach to study height zeta functions of projective spaces and projective bundles. To study height zeta functions of projective spaces Z(ℙⁿ, H_O(1); s), we apply the Riemann-Roch theorem of Arakelov vector bundles by van der Geer and Schoof to the integrand of an integral expression of Z(ℙⁿ, H_O(1); s). We give a proof of the analytic continuation and functional equations of height zeta functions of projective spaces with respect to various height functions. Motivic analogues of these results are also proved. We also study height zeta functions of Hirzebruch surfaces.

Citations

• Jacobians and symmetric products
• Rational points of bounded height on Fano varieties

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