Algebra Seminar

Tuesday, September 27, 2016
4:15 PM - 5:15 PM (ET)
Exley Science Center Tower ESC 618
Event Type
Rasmussen, Christopher

Bweong-Kweon Oh (Seoul National University): The number of representations of squares by integral quadratic forms

Abstract:  Let f be a positive definite integral ternary quadratic form and let r (k, f) be the number of representatives of an integer k by f. We say that the genus of f is indistinguishable by squares if for any integer n, r(n2, f) =  r(n, f ´) for any quadratic form f´ˊ in the genus of f. In this talk, we will give some examples of non trivial genera of ternary quadratic forms which are indistinguishable by squares. Also, we give some relations between indistinguishable genera by squares and a conjecture by Cooper and Lam, and we resolve their conjecture completely. This is a joint work with Kyoungmin Kim.


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