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Fearless Symmetry by Robert Gross, Avner Ash

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A
4
, 139–146
a
p
. See Legendre symbol
Abel, Niels, xxvi, 65, 90
Abelian group. See group, Abelian
absolute Galois group of Q, 92–102,
112, 139, 146–147, 257, 158–
259
absolute value, 34, 222
algebraic closure, 47–48
algebraic integer, 180
algebraically closed, 47, 91
associative law, 4
binary relation, 33
Birch, Bryan, 206
Birch–Swinnerton-Dyer Conjecture,
206, 231, 262
C (complex numbers), 47
c. See complex conjugation
χ. See character
(congruence), 33
Cantor, Georg, 90
character, 162–176
characteristic p,36
class field theory, 224
combinatorics, 234
compatible family, 230
complex conjugation, 46, 98
complex plane, 43
congruence, 33
congruent number problem, 110–111,
261–262
conjecture, 197–199, 231–232
conjugacy class, 165
corollary, 47
cuspidal normalized newform, 236,
245
cycle, 26–29, 140, 187
cycle decomposition, 26
cycle type, 187, 212–215
(discriminant), 182
| (divides), 185
Darmon, Henri, 255
definitions, 5–6
Deligne, Pierre, 232
De Moivre’s Theorem, 200
Descartes, Ren
´
e, 51, 67
determinant, 127, 130
Diophantine equation, 51
Diophantus, 51, 109
Dirichlet, Lejeune, 34
discriminant, 182
dot product, 117
(empty set), 69
E[n]. See elliptic curve, torsion
e (neutral element), 2
eigenvalue, 218
element, 5

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