Geodesic
On the Rank of Universal Quadratic Forms over Real Quadratic Fields
Documenta mathematica, Tome 23 (2018), pp. 15-34
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We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field Q(D​) and obtain lower and upper bounds for it in terms of certain sums of coefficients of the associated continued fraction. We also estimate such sums in terms of D and establish a link between continued fraction expansions and special values of L-functions in the spirit of Kronecker's limit formula.
DOI : 10.4171/dm/611
Classification : 11A55, 11E12, 11R11
Mots-clés : continued fraction, universal quadratic form, real quadratic form, number field, additively indecomposable integer, Kronecker's limit formula 
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     author = {V{\'\i}t\v{e}zslav Kala and Valentin Blomer},
     title = {On the {Rank} of {Universal} {Quadratic} {Forms} over {Real} {Quadratic} {Fields}},
     journal = {Documenta mathematica},
     pages = {15--34},
     year = {2018},
     volume = {23},
     doi = {10.4171/dm/611},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/611/}
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Vítězslav Kala; Valentin Blomer. On the Rank of Universal Quadratic Forms over Real Quadratic Fields. Documenta mathematica, Tome 23 (2018), pp. 15-34. doi: 10.4171/dm/611

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