Automorphic Forms and Sums of Squares over Function Fields

详细信息    查看全文

• 作者：Hoffstein ; Jeffrey ; Merrill ; Kathy D. ; Walling ; Lynne H.
• 刊名：Journal of Number Theory
• 出版年：1999
• 出版时间：December, 1999
• 年：1999
• 卷：79
• 期：2
• 页码：301-329
• 全文大小：206 K

文摘

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≥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.