The mass of shifted lattices and class numbers of inhomogeneous quadratic polynomials
Abstract
Abstract In this paper, we investigate class numbers of shifted quadratic lattices $L+\frac{\boldsymbol{u}}{c}$ with $\boldsymbol{u}\in L$ and odd conductor $c\in \mathbb{N}$. For a lattice $L$ whose genus only contains one class, we determine a lower bound for the number of classes in the genus of $L+\frac{\boldsymbol{u}}{c}$ depending on $c$. As a result, we obtain an explicit bound $c_{0}$ such that any such shifted lattice with one class in its genus must have conductor smaller than $c_{0}$, restricting the possible choices of such $L+\frac{\boldsymbol{u}}{c}$ to a finite set.
Fields of Study & Subjects
Analytic Number Theory Research
Analytic and geometric function theory
Meromorphic and Entire Functions
Publication details
- Journal / source
- International Mathematics Research Notices
- Volume
- 2026
- Issue
- 14
- Publication date
- 1 July 2026
- Language
- EN