Description
Number theory seminar II.
Speaker: Prasuna Bandi.
Affiliation: TIFR Mumbai.
Date and Time: Friday 25 October, 2:30 pm - 3:30 pm.
Venue: Ramanujan Hall, Department of Mathematics.
Title: Simultaneous density of integer values for an inhomogeneous
quadratic form and a linear form.
Abstract: In 1929 Oppenheim conjectured that for a nondegenerate,
indefinite, irrational quadratic form Q in n ≥ 5 variables, Q(Zn) is
dense in R. It was later strengthened to n ≥ 3 by Davenport and
proved in 1987 by Margulis based on Raghunathan’s conjecture on closures
of unipotent orbits.
Later, Dani and Margulis proved the simultaneous density at integer values
for a pair of quadratic and linear form in 3 variables when certain
conditions are satisfied. We prove an analogue of this for the case of an
inhomogeneous quadratic form and a linear form.