Roger BakerAffiliation: Brigham Young University Email: baker@math.byu.edu Title Of Talk: The values of quadratic forms at squarefree points URL: http:// Not available yet Abstract: I report on a project to obtain analogs of results of Heath-Brown on the representations of integers by quadratic forms in at least 3 variables. Heath-Brown uses a new form of the Hardy-Littlewood circle method, which he described in a Crelle paper in the nineties, and which has since been applied by himself, Hooley and the speaker. Briefly, one finds an asymptotic formula for the number of representations with smooth weights attached. In this project, all the variables have to be square-free, which makes matters a bit more complicated. In fact, in the paper I published on this in 2004, there were two cases (representing the value 0, quaternary form with determinant a square; and representing the value 0, ternary form) which I could not push through. I will report on my renewed efforts in these 'harder cases'.
Last update made Tue Jan 20 18:43:30 EST 2009.
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