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In this note, we give simple examples of sets $𝒮$ of quadratic forms that have minimal $𝒮$ -universality criteria of multiple cardinalities. This answers a question of Kim, Kim, and Oh [KKO05] in the negative.

Minimum of quadratic forms with respect to Fuchsian groups. II.

Asmus L. Schmidt (1977)

Journal für die reine und angewandte Mathematik

Minimum of quadratic forms with respect to Fuchsian groups. I.

Asmus L. Schmidt (1976)

Journal für die reine und angewandte Mathematik

Minkowskische Reduktionsbedingungen für positiv definite quadratische Formen in 5 Variablen.

L. Afflerbach (1982)

Monatshefte für Mathematik

Mixed sums of squares and triangular numbers

Zhi-Wei Sun (2007)

Acta Arithmetica

Mixed sums of squares and triangular numbers. II.

Suo, Song, Pan, Hao, Sun, Zhi-Wei (2007)

Integers

Modelování ve vědě a technice

Igor Vajda (1969)

Pokroky matematiky, fyziky a astronomie

Modular Forms of Half Integral Weight, Some Explicit Arithmetic.

A.G. van Asch (1983)

Mathematische Annalen

Modular Lagrangians and the theta multiplier.

Dennis Johnson, John J. Millson (1990)

Inventiones mathematicae

Modular lattices from finite projective planes

Tathagata Basak (2014)

Journal de Théorie des Nombres de Bordeaux

Using the geometry of the projective plane over the finite field $𝔽_{q}$ , we construct a Hermitian Lorentzian lattice $L_{q}$ of dimension $(q^{2} + q + 2)$ defined over a certain number ring $𝒪$ that depends on $q$ . We show that infinitely many of these lattices are $p$ -modular, that is, $p L_{q}^{'} = L_{q}$ , where $p$ is some prime in $𝒪$ such that ${| p |}^{2} = q$ .The Lorentzian lattices $L_{q}$ sometimes lead to construction of interesting positive definite lattices. In particular, if $q \equiv 3 mod 4$ is a rational prime such that $(q^{2} + q + 1)$ is norm of some element in $ℚ [\sqrt{- q}]$ , then we find a $2 q (q + 1)$ dimensional...

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Maximal Subgroups of the Finite Orthogonal and Unitary Groups Stabilizing Anisotropic Subspaces.

Mean square value of exponential sums related to the representation of integers as sums of squares

Mehrklassige Geschlechter von Einheitsformen in total reellen algebraischen Zahlkörpern.

Méthodes de factorisation et nombre de classes des corps quadratiques

Metrische G-Moduln über Körpern der Charakteristik 2.

Milnor’s conjecture on quadratic forms and $m o d; 2$ motivic complexes

Minimal forms with respect to function fields of conics.

Minimal $𝒮$ -universality criteria may vary in size