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
Noam D. Elkies 1; Daniel M. Kane 2; Scott Duke Kominers 3
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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},
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year = {2013},
doi = {10.5802/jtnb.848},
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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. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.848/
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