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 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 older, 8 Hua’s, 135 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 obius, 18 Mellin, 251 second 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
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