Index
Ap´ ery number, 199
Asymptotic formula for p(n), 86
Atkin-Lehner operator, 27, 51
Bailey pair, 167
Bernoulli numbers, 5
generalized, 14
Beukers’ supercongruence, 199
Birch and Swinnerton-Dyer Conjecture, 151
Borcherds’ isomorphism, 71
CM point, 70
Calabi-Yau threefold, 195
Central critical L-value, 150
Class equation, 130
Class number, 71, 133
Cohen and Lenstra heuristics, 134
Cohen-Eisenstein series, 15
Congruence subgroup, 1
Congruent number, 155
Crank of a partition, 89
Cusp, 2
Dedekind’s eta-function, 17
Degree of nilpotency, 34
Delta-function, 7
Denominator formula for the Monster, 25
Dimension formulas, 10, 16
Divisor function, 5
Divisor polynomial, 32
Dyson’s rank of a partition, 88
Eisenstein series, 5
Elliptic curve, 36, 150, 187, 190
congruent number, 151, 155, 157, 188
Legendre normal form, 187
quadratic twist of, 152
supersingular, 36
with complex multiplication, 188
Elliptic fixed point, 2
Eta-product, 18
Eta-quotient, 18
Euler’s generating function, 85
Filtration, 35
Fourier expansion, 4
Fricke involution, 27, 51
Fundamental domain of SL2( ), 1
Galois representation, 42, 63
Gaussian hypergeometric function, 184
Gauss sum, 201
Goldfeld’s Conjecture, 152
Gross-Koblitz formula, 201
Hecke eigenform, 22, 50
Hecke Gr¨ ossencharacter, 9
Hecke operator, 21, 49, 55
Hecke trace of singular moduli, 124
Heegner divisor, 70
Heine transformation, 166
Hurwitz class number, 71, 133
Hurwitz zeta-function, 175
Hypergeometric function, 166, 184
basic, 166
Gaussian, 184
ordinary, 183
Iwasawa λ-invariant, 139
Iwasawa µ-invariant, 139
j-function, 7
Jacobi sum, 184
Jacobi’s triple product identity, 17
K3 surface, 193
Kohnen newform, 55
Kohnen operator, 52
Kohnen plus space, 54
Koike’s Conjecture, 197
Kolyvagin’s Theorem, 151
L-function, 14
Dirichlet, 14
Hasse-Weil, 150
Kubota-Leopoldt, 134
modular, 149
Legendre normal form, 187
Lehmer’s Conjecture, 41
Modular curve, 109
215
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