Some new results in quantitative Diophantine approximation

Abstract

In this article we establish two new results on quantitative Diophantine approximation for one-parameter families of diagonal ternary indefinite forms. In the first result, we consider quadratic forms taking values at prime points. In the second, we examine inhomogeneous forms of arbitrary degree taking values at integer points.

Change in title, section 4 expanded and other minor edits. 24 Pages; accepted for publication in IMRN

References in corpus (3)

• Effective density for inhomogeneous quadratic forms I: generic forms and fixed shifts
• Effective density for inhomogeneous quadratic forms II: fixed forms and generic shifts
• Values of Inhomogeneous Forms at S-integral points