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| Murty R., Murty K. — Non-vanishing of L-Functions and Applications (Progress in Mathematics) |
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| Предметный указатель |
Algebraic number field 19
Alkin — Lehmer involution 81
Approximate functional equation 93
Aramata — Brauer theorem 30 35 40 183
Archimedean Euler factors 28
Artin conductor 28 44
Artin's conjecture 29 46 50 52 179 181 183
Artin's reciprocity theorem 29
Artin's theorem 36
Artin, E. 181
Ash, A. 190
Averages of higher derivatives 175
Balasubramanian, R. 94 95 125 127
Barban — Vehov weights 110 112
Barban, M.B. 112
Barthel, L. 189
Bateman, P.T. 141 154
Birch and Swinnertonn-Dyer conjectures 189
Boclmer, S. 178 180
Boecherer, S. 190
Borel subgroup 59
Brauer induction theorem 29
Brauer's induction theorem 182
Broecker, T. 67
Cartan subgroup 59 60
Cassels, J. 28
Character sums 132
Chebotarev density theorem 2 42 52 68 182
Chebycheff polynomials 88
Chowla, S. 141 154
Class function 25
Class number formula 16
Classification of primitive functions 184
Clifford's theorem 40
CM-type 83
Cohen, H. 80
Combinatorial identities 88
Compact groups 65 67—69
Compact Riemann surface 77 81
Congruence subgroup 76
Conjugacy class 27
Conrey, B. 178 180
Cusp forms 77 78 133
Cuspidal automorphic representations 189 190
Davenport, H. 42 117
Decomposition group 27
Dedekind's conjecture 30 32 183
Dedekind's zeta function 19 21 37 39 42 52 63 185
Deligne's Prime Number Theorem 68
Dieck, T. 67
DIMENSION 179
Dirichlet polynomial 2 116
Dirichlet series with positive coefficients 87
Discriminant 44
Eigenform 82
Eisenstein series 78
Elliptic curve 1 53 58
Elliptic curves over cyclotomic fields 190
Ellison, W. 15
Equicontinuity 65
Equidistribution 1 65 66
Erdoes — Turan inequality 71
Estimate of Rankin — Shahidi 138
Euler product 16 18 19 21 177
Explicit formula method 128
Factorization into primitives 179
Fainleib, A.S. 188
Fejer kernel 12
Fejer, L. 23
Foote, R. 35 39 41
Fourier inversion 11
Frey, G. 80
Friedberg, S. 140 190
Frobenius element 27
Frobenius reciprocity 25 30 31 36 43
Froehlich, A. 28 29
Functional equation 6 177
Fundamental discriminant 100 104 105 130 134 165 173 187
Furnsawa, M. 190
Galois module structure 29
Generalized ideal 22
Ghosh, A. 178 180
Ginzburg, D. 190
Goldfeld — Viola conjecture 189
Goldfeld, D. 187
Graham, S. 112 113
Haar measures 65 67 72 84
Hadamard factorization 38
Hadamard's proof 9
Heath-Brown, R. 95
Hecke operators 82
Hecke subgroup 76
Hecke's L-functions 21
Hecke's theorem 81
Hensel's estimate 44 46 49
Hensel's inequality 60
Higher ramification groups 28
Hilbert class field 55
Hildebrand, A. 96
Hoffman, J 190
Hoffstein, J. 140 190
Howe correspondence 189
Hyperbolic 76
Ideal class group 21
Ideal classes 21
Inductive property of L-functions 43
Inertia group 27
Inner product 78
Integrated Polya — Vinogradov estimate 141
Iwaniec, H. 176 187
Jacquet, H. 184
Jutila's character sum estimate 97
Jutila, M. 97 104 131 153
Kahiaue, Jean-Pierre 9
Katz, N. 53
Kernel function 53
Knapp A. 80
| L-function formalism 35
Lagarias, J. 42 44 48 54 61
Lang, S. 92
Langlands program 84
Large sieve inequality 117 175
Least prime in a conjugacy class 52
Line integral 6
Luo, W. 190
Mackey's theorems 26
Mean-value estimate of Jutila 131
Merel, L. 190
Metaplectic Eisenstein series 140
Method of averages 2
Minimal normal subgroup 34
Modular curve 77
Modular elliptic curve 3
Modular forms 1 77
Modular L-functions 2
Mollifier polynomial 116
Monomial characters 33 61
Montgomery, H. 44 54 72
Montgomery, H.L. 97 154
Murty, M.Ram 35 46 85 95 128 134 136 137 140 147 153 159 179 185 189
Murty, V.Kumar 9 35 39 46 48 77 84 95 125 127 134 136 137 140 147 153 159 185 189
Newforins 83
Non-abelian L-functions 181
Normalized eigenfunctions 82
Odlyzko, A.M. 42 44 48 54 61
Oesterle, J. 80
Ogg, A. 82 84
Omega theorem 88
Oscillation of Fourier coefficients 2 75 81
Otdforms 83
Parabolic 76
Parseval's formula 12
Perelli, A. 187
Peter — Weyl theorem 66
Petersson inner product 83
Piatetski-Shapiro, I. 189
Polya — Vinogradov estimate 95 97 129 130 139
Polya — Vinogradov inequality 97 137
Polya-Vinogradov 95
Pomykala, J. 187
Positive proportion 127
Prime ideal theorem 20
Prime number theorem 2 5 6
Primes in arithmetic progression 15
Primitive function 178
Principal congruence subgroup 75
Quadratic twists 133
Ramakrislman, D. 189 190
Ramanujan conjecture 75 83 184
Ramanujan — Petersson conjecture 84
Ramanujan's cusp form 79
Rankin — Selberg convolution 140
Rankin's estimate 166
Rankin's theorem 90
Rankin, R. 90 137 138
Ray class characters 190
Ray class group 21 22
Real character sums 152
Regular representation 26
Relative discriminant 44
Rhoades, S. 35 61
Riemann hypothesis 11 95 97 128 129
Riemann zeta function 177 183
Riemann — Lebesgue lemma 12 13
Rohrlich, D. 134 190
Rudin, W. 11
Rudnick, Z. 190
Saparnijazov, O. 138
Saradha, N. 46
Sarnak, P. 190
Sato — Tate conjecture 2 83 84 91
Scherk, J. 46
Schulze-Pillot, R. 190
Selberg eigenvalue, conjecture 183 190
Selberg's class 177
Selberg's conjectures 3 177
Selberg, A. 177 178 180
Semidirect product 34
Serre, J.-P. 26 42 61 65 68 83
Shahidi, F. 90
Shalika, J.A. 184
Shimura, G. 80 134
Siegel, G.L. 95
Smooth approximation 98
Smoothing operator 163
Stark, H.M. 35 37 38
Stefanicki, T. 140 187 189
Stirling's formula 118
Supersolvable group 61
Tate's thesis 22
Tauberian theorem 11 19 88
Tauberian theory 2
Theorem of Brauer 29
Trigonometric identities 86
Trigonometric inequality 2
Trigonometric lemma 69
Uchida, K. 32
Uniform distribution 2
Unique factorization of L-functions 182
Upper bounds for torsion 190
Upper half-plane 76
van der Waall, R.W. 32
Vaughan, R.C. 97 154
Vehov, P.P. 112
Vigneras, M.F. 179
Vinogradov's lemma 98 100
Vinogradov, I.M. 98 100
Viola, C. 187
Waldspurger, J. 134
Wales, D. 41
Weighted sums 137 158 187
Weil's conjectures 75
Weil's criterion 67
Wiener — Ikehara tauberian theorem 7 8 68
Zhang, Y. 189
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