Automorphic forms and sums of squares over function fields

[摘要] We develop some of the theory of automorphic forms in the function field setting. As an application, we find formulas for the number of ways a polynomial over a finite field can be written as a sum of k squares, k greater than or equal to 2. As a consequence, we show every polynomial can be written as a sum of 4 squares. We also show, as in the classical case, that these representation numbers are asymptotic to the Fourier coefficients of the basic Eisenstein series. (C) 1999 Academic Press.

[发布日期] 1999-12-01