Regular Article: Newton Polygons of L Functions Associated with Exponential Sums of Polynomials of Degree Four over Finite Fields
Regular Article: Newton Polygons of L Functions Associated with Exponential Sums of Polynomials of Degree Four over Finite Fields
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DOI：
10.1006/ffta.2000.0287
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发表时间：
2001
影响因子：
1
通讯作者：
Shaofang Hong
中科院分区：
文献类型：
--
作者：
Shaofang Hong
Let F"q be the finite field of q elements with characteristic p and F"q"^"m its extension of degree m. Fix a nontrivial additive character @J of F"p. If f(x"1,..., x"n)@?F"q[x"1,..., x"n] is a polynomial, then one forms the exponential sum S"m(f)=@?"("x"""1","...","x"""n")"@?"("F"q"^"m")"^"n@J(Tr"F"""q"""^"""m"/"F"""p(f(x"1,...,x"n))). The corresponding L functions are defined by L(f, t)=exp(@?^~"m"="0S"m(f)t^m/m). In this paper, we apply Dwork's method to determine the Newton polygon for the L function L(f(x), t) associated with one variable polynomial f(x) when deg f(x)=4. As an application, we also give an affirmative answer to Wan's conjecture for the case deg f(x)=4.
