Biases towards the zero residue class for quadratic forms in arithmetic progressions
Abstract
Abstract We prove a bias towards the zero residue class in the distribution of the integers represented by binary quadratic forms. In most cases, we prove that the bias comes from a secondary term in an associated asymptotic expansion. This is unlike Chebyshev's bias, which exists somewhere at the level of . We make a conjecture on the general situation which includes all cases not proven. Results on the distribution of the integers represented by a quadratic form—some of which are of independent interest—are proven along the way. The paper concludes with some numerical data that is illustrative of the bias.
Fields of Study & Subjects
Analytic Number Theory Research
Mathematical Approximation and Integration
Publication details
- Journal / source
- Mathematika
- Volume
- 72
- Issue
- 2
- Publication date
- 1 April 2026
- Language
- EN