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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