Research Highlights

On values of isotropic quadratic forms

Authors :- Choudhuri M.; Makadiya P.J.

Publication :- Boletin de la Sociedad Matematica Mexicana, Volume 30, article number 16, (2024).

Let K be a locally compact non-discrete field of characteristic and Q be a non-degenerate isotropic binary quadratic form with coefficients in K. We obtain asymptotic estimates for the number of solutions in the two-fold product of a discrete subring inside K, of the inequalities of the form for some where is an ultrametric absolute value on K. The estimates are obtained in terms of continued fraction expansions of the coefficients of the quadratic form Q.