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].
Published online:
DOI: 10.5802/jtnb.848
Classification: 11E20, 11E25
Keywords: 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/} }
TY - JOUR TI - Minimal $\mathcal{S}$-universality criteria may vary in size JO - Journal de Théorie des Nombres de Bordeaux PY - 2013 DA - 2013/// SP - 557 EP - 563 VL - 25 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.848/ UR - https://zbmath.org/?q=an%3A1286.11046 UR - https://www.ams.org/mathscinet-getitem?mr=3179676 UR - https://doi.org/10.5802/jtnb.848 DO - 10.5802/jtnb.848 LA - en ID - JTNB_2013__25_3_557_0 ER -
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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