216 INDEX
Modular form, 3, 3, 4
complex multiplication, 9
half-integral weight, 11
holomorphic, 3, 11
integral weight, 3
meromorphic, 3, 11
newform, 29
p-adic, 74
weakly holomorphic, 3, 11
Modular function, 3
Nebentypus character, 4, 11
Newform, 29, 55
Newman’s Conjecture, 105
p-adic Γ-function, 199
Parkin-Shanks Conjecture, 101
Partition, 85
function p(n), 85
Petersson inner product, 29
Projection operator, 51
Quadratic twist, 22, 52
of an elliptic curve, 152
of a modular form, 22, 52
Ramanujan’s 1Ψ1 summation, 166
Ramanujan’s congruences for p(n), 87
Ramanujan-Petersson Conjecture, 31
Ramanujan’s tau-function, 41
Ramanujan’s Theta-operator, 23, 36
Rank of a partition, 88
Rogers-Fine identity, 166
Selmer group, 157
Shafarevich-Tate group, 157
Shimura correspondence, 53
Shimura-Taniyama Conjecture, 151
Siegel-Walfisz condition, 144
Sign of the functional equation, 150
Singular K3 surface, 193
Singular modulus, 121
Slash operator, 3, 51
Sturm’s Theorem, 40
Subbarao’s Conjecture, 102
Supersingular j-invariant, 36
Teichm¨ uller character, 135, 201
Theta function, 12
Theta operator, 23, 36
Traces of Hecke operators, 196
Traces of singular moduli, 124
Trinomial coefficient, 196
Twist of a modular form, 22, 52
U -operator, 28, 50
V -operator, 28, 50
Valence formula, 8
Weierstrass point, 109
Weierstrass weight, 109
Previous Page Next Page