Euclidean lattices, theta invariants, and thermodynamic formalism

DOI10.1007/978-3-030-57559-5_5zbMath1458.11112arXiv1909.04992OpenAlexW3134172667MaRDI QIDQ2019720

Jean-Benoît Bost

Publication date: 22 April 2021

Full work available at URL: https://arxiv.org/abs/1909.04992

Mathematics Subject Classification ID

Introductory exposition (textbooks, tutorial papers, etc.) pertaining to algebraic geometry (14-01) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to number theory (11-01) Geometry of numbers (11Hxx)

Cites Work

• Korkin-Zolotarev bases and successive minima of a lattice and its reciprocal lattice
• Optimality and uniqueness of the Leech lattice among lattices
• Reduction theory using semistability
• Explicit Tauberian estimates for functions with positive coefficients
• Eine Bemerkung zur Reduktionstheorie quadratischer Formen
• New bounds in some transference theorems in the geometry of numbers
• Analytische Zahlentheorie in Körpern der Charakteristik \(p\)
• The Gaussian core model in high dimensions
• An arithmetic analogue of Clifford's theorem
• Integral representations of unramified Galois groups and matrix divisors over number fields
• Minima of Epstein's zeta function and heights of flat tori
• Lattice points in high-dimensional spheres
• Hermitian vector bundles and extension groups on arithmetic schemes. I: Geometry of numbers
• Lattices and Codes
• A Note on a Classical Theorem of Blichfeldt
• A reverse Minkowski theorem
• Theta Invariants of Euclidean Lattices and Infinite-Dimensional Hermitian Vector Bundles over Arithmetic Curves
• Numerical cohomology
• An Inequality for Gaussians on Lattices
• Dimension reduction techniques for the minimization of theta functions on lattices
• The Difference between Consecutive Prime Numbers
• A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the sum of Observations
• Probability Theory
• Convexity
• Notions of convexity
• Effectivity of Arakelov divisors and the theta divisor of a number field
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