A Tight Reverse Minkowski Inequality for the Epstein Zeta Function

We prove that if L ⊂ Rn is a lattice such that det(L′) ≥ 1 for all sublattices L′ ⊆ L, then ∑

[1]  Noah Stephens-Davidowitz,et al.  Kissing Numbers and Transference Theorems from Generalized Tail Bounds , 2018, SIAM J. Discret. Math..

[2]  ACTA ARITHMETICA , 2022 .

[3]  Barak Weiss,et al.  A volume estimate for the set of stable lattices , 2014 .

[4]  F. Thorne,et al.  Geometry of Numbers , 2017, Algebraic Number Theory.

[5]  Peter Sarnak,et al.  Minima of Epstein’s Zeta function and heights of flat tori , 2006 .

[6]  Masoud Abbaszadeh,et al.  Number 37 , 1978 .

[7]  Daniel Dadush,et al.  Towards Strong Reverse Minkowski-Type Inequalities for Lattices , 2016, 2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS).

[8]  Oded Regev,et al.  A reverse Minkowski theorem , 2016, STOC.

[9]  N. Sheibani,et al.  Paris , 1894, The Hospital.

[10]  J. G. Corput.  Verallgemeinerung einer Mordellschen Beweismethode in der Geometrie der Zahlen , 1935 .