Uniform bounds for lattice point counting and partial sums of zeta functions

DOI10.1007/s00209-021-02862-zzbMath1489.11099arXiv1710.02190OpenAlexW3207942902MaRDI QIDQ2114161

David Lowry-Duda, Frank Thorne, Takashi Taniguchi

Publication date: 15 March 2022

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02190

zbMATH Keywords

zeta functionslattice point countingpartial sums.

Mathematics Subject Classification ID

Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Lattices and convex bodies (number-theoretic aspects) (11H06) Heights (11G50) Lattice points in specified regions (11P21)

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Cites Work

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• Secondary terms in counting functions for cubic fields
• The Schanuel theorem in adelic Hermitian bundles
• On zeta functions associated with prehomogeneous vector spaces
• On lattice sums and Wigner limits
• Functional equations with multiple gamma factors and the average order of arithmetical functions
• An introduction to the geometry of numbers.
• Explicit Upper Bounds for Residues of Dedekind Zeta Functions and Values ofL-Functions ats= 1, and Explicit Lower Bounds for Relative Class Numbers of CM-Fields
• On the lattice point problem for ellipsoids
• Counting primitive points of bounded height
• Explicit counting of ideals and a Brun–Titchmarsh inequality for the Chebotarev density theorem
• Summation Formulae for Coefficients of L-functions
• On a Principle of Lipschitz