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