Height of flat tori

DOI10.1090/S0002-9939-97-03872-0zbMath0905.11035MaRDI QIDQ4333004

Patrick Chiu

Publication date: 19 February 1997

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

Kronecker's limit formulaEpstein zeta functiondeterminant of the Laplacianminima of quadratic formsheight of a Riemannian manifoldheight of flat toriminimum height

Mathematics Subject Classification ID

Lattices and convex bodies in (n) dimensions (aspects of discrete geometry) (52C07) Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Lattices and convex bodies (number-theoretic aspects) (11H06) Global Riemannian geometry, including pinching (53C20) Dedekind eta function, Dedekind sums (11F20) Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. (explicit formulas) (11M36) Quadratic forms (reduction theory, extreme forms, etc.) (11H55) Minima of forms (11H50)

Related Items

Kronecker's limit formula and the height of Euclidean lattices ⋮ The height of the Leech lattice ⋮ On similarity classes of well-rounded sublattices of \(\mathbb Z^2\) ⋮ Spherical designs and heights of Euclidean lattices ⋮ The BCC Lattice in a Long-Range Interaction System ⋮ Three‐dimensional lattice ground states for Riesz and Lennard‐Jones–type energies ⋮ Crystallization for Coulomb and Riesz interactions as a consequence of the Cohn-Kumar conjecture ⋮ Renormalized energy and asymptotic expansion of optimal logarithmic energy on the sphere ⋮ Extremal metrics for spectral functions of Dirac operators in even and odd dimensions ⋮ Towards physically motivated proofs of the Poincaré and geometrization conjectures ⋮ Zeta functions, heat kernels, and spectral asymptotics on degenerating families of discrete tori ⋮ Minima of Epstein's zeta function and heights of flat tori ⋮ A negative mass theorem for the 2-torus ⋮ Universal optimality of the \(E_8\) and Leech lattices and interpolation formulas

Cites Work

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• A lemma about the Epstein zeta-function
• A Minimum Problem for the Epstein Zeta-Function