Counting Polynomials representable as sum of squares, an analogue of a classical theorem of Landau
Chih-Yun Chuang ( Taida Institute for Mathematical Sciences )
2017-07-28 12:30 - 13:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
An analogue over Fq[T] of Landau’s theorem on sums of two squares was considered by Bary-Soroker, Smilansky and Wolf. They counted the number the number of monic polynomials in Fq[T] of degree n of the form A^2+TB^2, which we denote by B(n,q). Gorodetsky obtains an nice asypototic formula of B(n,q), as q^n goes to infinity,for an explicit constant Kq =1+O(1/q). He also applies his method to improving C.,Kuan and Yu’s previous result of “On counting polynomials over ﬁnite ﬁelds. ”In this talk,we use another method to approach Gorodetsky’s result and generalize it. This is a joint work with Yen-Liang Kuan.