Index

absolute inner product, 6.5

adjoint operator, 6.4

ambiguous class, 12.5

angle of a Kloosterman sum, 4.4

Artin conjecture, 12.6

Artin L-function, 12.6

automorphic form, 2.7

automorphs of a quadratic form, 11.2

Bernoulli numbers, 1.3

B-group of integral translations, 2.5

chart, 2.3

circle method of Kloosterman, 11.4

class group, 12.2

class group L-function, 12.4

complete L-function, 7.2

complex conjugation operator K, 6.7

congruence group, 2.4

congruent number, 8.2

congruent theta function, 10.1

conjugacy class, 2.2

consistency condition, 2.6

converse theorem, 7.4

convolution L-functions, 13.1

criterion for cusp forms, 7.4

cusp, 2.3

cusp form, 2.7

cusp forms for the modular group, 1.6

cuspidal zone, 2.3

decomposition group, 12.6

Dedekind sum, 2.8

Dedekind zeta-function, 12.2

deformation factor, 2.1

determinant of a quadratic form, 11.2

diagonal symbol, 5.5

different of a field, 12.2

differential operator of Euler, 9.2

Dirichlet class number formula, 11.2

discontinuous group, 2.3

discrete group, 2.3

discriminant function, 1.2

discriminant of a field, 12.2

discriminant of a quadratic form, 11.2

discriminant of an elliptic curve, 8.1

double cosets, 2.5

eigenvalue r\ of W, 6.7

Eisenstein series E(z,Q), 11.3

Eisenstein series for the modular group, 1.3

Eisenstein series of weight zero, 13.2

Eisenstein series with a multiplier, 3.2

ellipsoid KA, 9.1

elliptic curve, 8.1

elliptic function, 1.2

elliptic, hyperboic, parabolic motions, 2.2

equidistribution, 11.6

equivalence class of forms, 11.2

equivalent quadratic forms, 11.2

eta-function, 2.8

Euler product for Hecke L-function, 6.8

even quadratic form A[x], 10.1

factor system of weight k, 2.6

Fourier coefficient at a cusp, 2.7

Fourier expansion at a cusp, 2.7

Fourier transform, 1.1

fractional part, 1.1

Fricke involution W, 6.7

Frobenius automorphism, 12.6

Frobenius conjugacy class, 12.6

Fuchsian group, 2.3

Fuchsian group of the first kind, 2.3

functional equation for Hecke L-function, 7.2

fundamental domain, 2.3

fundamental units, 12.2

gamma function, 7.1

Gauss sum, 4.3

Gauss sum W ( 0 , 12.2

generating function of Poincare series, 3.1

genus characters, 12.5

genus group, 12.5

genus mass, 11.2

genus of quadratic forms, 11.2

geodesies, 2.1

Grossencharacter, 12.2

group of fractional ideals, 12.2

harmonic function, 9.2

harmonic polynomial, 9.2

Hasse-Weil L-function, 8.1

Hecke congruence group, 2.4

Hecke eigencuspform, 6.6

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