### Philadelphia Area Number Theory Seminar

Wednesday, October 11, 2017 - 2:15pm

#### Alicia Marino

University of Hartford

An integral quadratic form is said to be strictly k-regular if it primitively represents all quadratic forms of k variables that are primitively represented by its genus. We show that, for k > 1, there are ﬁnitely many inequivalent positive deﬁnite primitive integral quadratic forms of k + 4 variables that are strictly k-regular. This joint work with W.K. Chan extends a recent ﬁniteness result of Andrew Earnest et al. (2014) on strictly regular quadratic forms of 4 variables.