Minimal đť’®-universality criteria may vary in size
Noam D. Elkies1; Daniel M. Kane2; Scott Duke Kominers3
1Department of Mathematics Harvard University One Oxford Street Cambridge, MA 02138
2Department of Mathematics Stanford University Building 380, Sloan Hall Stanford, California 94305
3Society 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
Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 3, pp. 557-563

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.

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].

Received:
Published online:
DOI: 10.5802/jtnb.848
Classification: 11E20, 11E25
Keywords: universality criteria, quadratic forms

Noam D. Elkies  1 ; Daniel M. Kane  2 ; Scott Duke Kominers  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 
Noam D. Elkies; Daniel M. Kane; Scott Duke Kominers. Minimal $\mathcal{S}$-universality criteria may vary in size. Journal de théorie des nombres de Bordeaux, Volume 25 (2013) no. 3, pp. 557-563. doi: 10.5802/jtnb.848
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