Contents
Chapter 1 Introduction 1
Chapter 2 A Sketch of Kloosterman Sums 7
Chapter 3 PPs with st ≡r(mod pn-1) 13
3.1 PPs with s(pm+1) ≡pm+1(mod p2m-1) 13
3.2 PPs with s(pm-1) ≡pm-1(mod p2m-1) 47
3.3 Other PPs of the form (1.1) with st ≡r(mod pn-1) 57
3.4 PPs from trace functions with st ≡r(mod pn-1) 65
Chapter 4 PPs with Fractional Exponent s 72
4.1 PPs with fractional exponent s= +pil 73
4.2 PPs with fractional exponent s= +pil 83
4.3 PPs with fractional exponent s= 4+pil 90
4.4 PPs with fractional exponent s= +pil 93
4.5 PPs with fractional exponent s= +pil 96
Chapter 5 PPs of the Form 110
5.1 PPs f(x) from permutations 112
5.2 PPs f(x) over Fpn with s1 ≡pts2(modpm-1) 114
5.2.1 PPs over Fpn with s1 ≡s2(mod pm-1) 114
5.2.2 PPs f(x) over F2n with s1 ≡2ts2(mod 2m-1) for t>0 129
5.3 PPs f(x) with fractional s1 and s2 134
5.4 Other PPs f(x) over Fpn 141
Chapter 6 Other PPs 142
Bibliography 161
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