Number Theory: An Introduction to Mathematics

588 Notations

B,74

^2 ,L^2 (I),75

∗R,76

b|a,b
a,×,(a,b),83

[a,b], 84

a∧b,a∨b,85

(a 1 ,a 2 ,...,an),[a 1 ,a 2 ,...,an], 86

K[t], 87, 96

K(t), 88, 262

mCn, 92, 111

∂(f),|f|,R[t],R[[t]], 96

K[t,t−^1 ], 98

c(f), 100

R[t 1 ,...,tm], 101

Φp(x), 102

f′, 103

δ(a), 104

Q(

√

d),Od, 105

a≡bmodm,≡, 106

Z(m), 107

Z×(m), 108

Fp,φ(m), 109

Φn(x), 111, 112

f ̄(x), 111

F×p, 114

G,N(γ), 119

H,γ ̄, 120

N(γ),(α,β)r, 121

x,g(k),w(k), 122

G(k), 123

K[[t 1 ,...,tm]], 124

Fq, 125

(a/n),sgn(πa), 130

(a/p), 133

G(m,n), 137

Q(

√

d),α′, 140
N(α),ω,Od,G,E, 141
(a 1 ,...,am),AB, 145
A′, 146
h(d),O(K), 151
f∗g, 152
δ(n),A,|f|, 153
i(n),j(n), 154
τ(n),σ(n), 155
μ(n),fˆ(n), 156

Mp, 158

γ, 159, 380

Fn, 160

GLn(Z), 162

A⊕B, 163, 301

M 1 ∩M 2 ,M 1 +M 2 , 166

∆k, 171

|a|, 173

(f/g), 174

ξ,ξn,τ, 179

[a 0 ,a 1 ,a 2 ,...], 179, 182, 212

pn,qn, 180

pn/qn, 181, 212

[a 0 ,a 1 ,...,aN], 182

M(ξ), 190

D, 191

ζ′, 192

[a 0 ,...,am− 1 ,am,...,am+h− 1 ], 192

C, 198

H, 201

Γ,SL 2 (Z),T(z),S(z), 202

R(z),∂(F), 203

F ̄, 204

τ(f), 206

h†(D), 206, 207

H/Γ, 209, 218

Γ(n),ξ(k),μk, 210

|f|,f,{f}, 211

PSL 2 (R), 218

detA, 224-229

Mn,diag[α 11 ,α 22 ,...,αnn], 225

SLn(F),At, 226, 229

‖v‖, 229, 234

A⊗B, 231

Jm, 232, 248

em, 233, 248

2-(v,k,λ), 247

t-(v,k,λ), 250

Cp,An,PSLn(q), 251

M 12 ,M 11 ,M 24 ,M 23 ,M 22 , 251

|x|, 254

[n,k,d],C(H),G 24 ,R( 1 ,m), 255

Cζ((z)),Cζ[[z]],|a|, 261

|a|∞,vp(a),|a|p,K(t), 262