In this note, we give simple examples of sets of quadratic forms that have minimal -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 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].
Keywords: universality criteria, quadratic forms
Elkies, Noam D. 1 ; Kane, Daniel M. 2 ; Kominers, Scott Duke 3
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author = {Elkies, Noam D. and Kane, Daniel M. and Kominers, Scott Duke},
title = {Minimal $\mathcal{S}$-universality criteria may vary in size},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {557--563},
year = {2013},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {25},
number = {3},
doi = {10.5802/jtnb.848},
zbl = {1286.11046},
mrnumber = {3179676},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jtnb.848/}
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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
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