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The Quarterly Journal of Mathematics Advance Access published online on May 29, 2009
The Quarterly Journal of Mathematics, doi:10.1093/qmath/hap019
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© 2009. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oxfordjournals.org

ON THE NUMBER OF SQUARES REPRESENTED BY A PRODUCT OF TWO TERNARY QUADRATIC FORMS

Ritabrata Munshi{dagger}

Department of Mathematics, Rutgers University, 110 Frelighuysen Road, Piscataway, NJ 08854, USA

{dagger} E-mail: rmunshi{at}math.rutgers.edu

Received 16 February 2009; revised 30 April 2009
  Abstract

In the context of Manin's conjecture it is an important problem to estimate the number of times a ternary quartic form represents a square. In this paper we give good estimates for this counting problem when the quartic form is a product of two ternary quadratic forms.


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