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.

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DOI : https://doi.org/10.5802/jtnb.848
Classification : 11E20,  11E25
Mots clés : universality criteria, quadratic forms
@article{JTNB_2013__25_3_557_0,
     author = {Noam D. Elkies and Daniel M. Kane and Scott Duke Kominers},
     title = {Minimal $\mathcal{S}$-universality criteria may vary in size},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {557--563},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {25},
     number = {3},
     year = {2013},
     doi = {10.5802/jtnb.848},
     zbl = {1286.11046},
     mrnumber = {3179676},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.848/}
}
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, Tome 25 (2013) no. 3, pp. 557-563. doi : 10.5802/jtnb.848. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.848/

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