Office: Neckers 279
Email: aearnest at math.siu.edu
Professor, Ph.D., Ohio State University, 1975. Algebra, Algebraic Number Theory, and Arithmetic Theory of Quadratic Forms.
My primary research interest lies in the integral theory of quadratic forms, a classical area of number theory with contemporary applications in such mathematical fields as coding theory, topology and finite group theory. Much of my work has focused on the properties of spinor genera of quadratic forms and on the representation of integers by spinor genera and by individual quadratic forms. I have also maintained an interest in the special properties of binary quadratic forms and the associated structures in ideal class groups.
- The representation of binary quadratic forms by positive definite quaternary quadratic forms, Trans. Amer. Math. Soc. 345 (1994), 853-863.
- Two-element generation of orthogonal groups over finite fields, with H. Ishibashi, J. Algebra 165 (1994), 164-171.
- Universal and regular positive quadratic lattices over totally real number fields, Integral quadratic forms and lattices (Seoul, Korea, 1998), Contemp. Math. 249 (1999), 17-27.
- Discriminant bounds for spinor regular ternary quadratic lattices, with W.K. Chan, J. London Math. Soc. 69 (2004), 545-561.
- Represented value sets for integral binary quadratic forms and lattices, with R.W. Fitzgerald, Proc. Amer. Math. Soc. 135 (2007), 3765-3770.