Index 367
Gross, B., 205
group
character of, 76
circle, 82
general linear, 71
of characters, 96
group representation, 71
adjoint, 79
completely reducible, 73
degree of, 71
direct sum, 72
equivalence of, 71
irreducible, 73
isotypical components of, 74
linear map of, 71
matrix entries of, 74
regular, 78
representation space of, 71
subrepresentation of, 72
trivial, 71
unitary, 74, 79
Grupp, F., 30
Guinand, A. P.
-Weil formula, 316
H¨ older, O., 109
Hadamard, J. S., 1, 159, 166, 177
factorization theorem, 238
Hall divisor, 36
Hall, R. R., 26
Hanson, D., 34
Hardy, G. H., xiv, 32, 46, 55, 67, 144
Circle Method, 144
Harman, G., 29, 286
harmonics, 68
Heath-Brown, D. R., 28, 29, 101, 102,
143, 149, 177, 205, 245, 285
Hecke, E., 269
theta formula, 260
Heilbronn, H. A., xiv, 29, 323
theorem of, 269
Helson, H., 99
Hilbert, D., 112, 148, 150
-Waring theorem, 143
Hildebrand, A. J., 102, 179
Hoheisel, G., 29
Hooley, C., 102, 149
Horn, R. A., 101
Hua, L. K., 148, 178
lemma, 135
Hurwitz, A., 247
Huxley, M. N., 29, 30, 32
Hypothesis H, 101
identity
convolution, 17, 18
Euler, 60
Jacobi quartic, 250
Legendre, 2
partial summation, 10
Ikehara, S.
Tauberian theorem of, 281
imprimitive character, 91
inclusion and exclusion principle, 28
indicator function, 43
induced
character, 294
representation, 293
inequality
Bessel’s, 210
Cauchy-Schwarz, 9
Chebyshev, 46
H¨ older, 8
Hua’s, 135
P´ olya-Vinogradov, 93
Weyl, 132
inflation of a character, 296
Ingham, A. E., xiv, 29, 179, 323
integer part function, 2
integral logarithm, 1
invariant subspace, 72
inverse under Dirichlet convolution, 18
inversion formula
first M¨ obius, 18
Mellin, 251
second M¨ obius, 19
isotypical components, 74
Iwaniec, H., 28, 29, 32, 67, 100, 101, 223
Jacobi, C. G. J.
quartic identity, 250
theta function, 216, 249
Jensen, J. L. W. V., 99
Jensen’s formula, 236
Joly, J.-R., 116
Jutila, M., 29
Kac, M., 43, 48
Kahane, J.-P., 223
Kalm´ ar, L., 34
Kempner, A., 148
Kersey, J., 16, 31
Kinkelin, H., 247
Kloosterman, H. D., 113, 145
