Title
The representation of integers by positive ternary quadratic polynomials
Department
Mathematics
Document Type
Article
Publication Source
Journal of Number Theory
Publication Date
2015-11-01
Volume
156
First Page
75
Last Page
94
Abstract
© 2015 Elsevier Inc. An integral quadratic polynomial is called regular if it represents every integer that is represented by the polynomial itself over the reals and over the p-adic integers for every prime p. It is called complete if it is of the form Q(x+v), where Q is an integral quadratic form in the variables x=(x1, . . ., xn) and v is a vector in Qn. Its conductor is defined to be the smallest positive integer c such that cv∈Zn. We prove that for a fixed positive integer c, there are only finitely many equivalence classes of positive primitive ternary regular complete quadratic polynomials with conductor c. This generalizes the analogous finiteness results for positive definite regular ternary quadratic forms by Watson [18,19] and for ternary triangular forms by Chan and Oh [8].
Keywords
Polynomials, Representations of quadratic
DOI
10.1016/j.jnt.2015.03.007
Recommended Citation
Chan, Wai Kiu and Ricci, James, "The representation of integers by positive ternary quadratic polynomials" (2015). Articles & Book Chapters. 231.
https://digitalcommons.daemen.edu/faculty_scholar/231
https://doi.org/10.1016/j.jnt.2015.03.007