We study the exponential sums of Dickson polynomials of the first kind over finite fields. We provide an explicit expression for these sums by utilizing a decomposition of these polynomial sums, character orthogonality, and an elementary norm identity to cancel out trivial characters. We then apply Weil-type Kloosterman estimates for the remaining non-trivial character sums to obtain a bound, which is sharper than the Weil bound in all possible cases. This is joint work with Daqing Wan.

丁治国，现为湖南师范大学教授，曾就职于国防科技大学，中南大学。丁治国教授于中国科学院获得博士学位，研究方向为数论。他长期与国际知名数学家Michael Zieve 合作，在有限域的算术领域做出了一系列杰出工作，研究成果发表于Proc. Lond. Math. Soc.,  Int. Maht. Res. Not.，Science China Math.,  J. Comb. Theory A.，J. Number Theory,  J. Algebra等著名期刊，获得了国内外同行的广泛认可，并曾受邀在第十届世界华人数学家大会（ICCM2025）作报告。