Minimal 𝒮-universality criteria may vary in size
Journal de théorie des nombres de Bordeaux, Tome 25 (2013) no. 3, pp. 557-563.

Nous donnons des exemples simples d’ensembles 𝒮 de formes quadratiques qui ont des critères d’universalité minimaux de plusieurs cardinalités. Nous donnons ainsi une réponse négative à une question de Kim, Kim et Oh [KKO05].

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.

DOI : 10.5802/jtnb.848
Classification : 11E20, 11E25
Mots clés : universality criteria, quadratic forms
Elkies, Noam D. 1 ; Kane, Daniel M. 2 ; Kominers, Scott Duke 3

1 Department of Mathematics Harvard University One Oxford Street Cambridge, MA 02138
2 Department of Mathematics Stanford University Building 380, Sloan Hall Stanford, California 94305
3 Society of Fellows Dpt of Economics Program for Evolutionary Dynamics Center for Research on Computation and Society Harvard University One Brattle Square, Suite 6 Cambridge, MA 02138-3758
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Elkies, Noam D.; Kane, Daniel M.; Kominers, Scott Duke. Minimal $\mathcal{S}$-universality criteria may vary in size. Journal de théorie des nombres de Bordeaux, Tome 25 (2013) no. 3, pp. 557-563. doi : 10.5802/jtnb.848. http://www.numdam.org/articles/10.5802/jtnb.848/

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