364 Index Cashwell, E. D., 64, 99 Cauchy, A. L. -Davenport-Chowla theorem, 141 Chandrasekharan, K., 98, 222 character Dirichlet, 84 conductor of, 91 even, 109 imprimitive, 91 induced, 91 nonprincipal, 85 primitive, 91 principal, 85 quasiperiod of, 91 real, 109 group, 76, 96 degree of, 78 inflation of, 296 real, 77 regular, 78 trivial, 76 induced, 294 table, 107 Chebyshev, P. L., 29, 33 inequality, 46 method of, 3, 19 psi function, 2 theta function, 2 Chen, J. R., 28 Chevalley, C. -Warning theorem, 151 Chih, T.-T., 32 Chowla, I. Cauchy-Davenport-Chowla thm., 141 Chudakov, N. G., 29, 178 Cipolla, M., 31 circle group, 82 class functions, 76 class number formula analytic, 267 Dirichlet, 270 classical Fourier series, 68 classical Gauss sum, 70, 222 Cojocaru, A. C., 28 completed L-function, 231 conductor of a Dirichlet character, 91 Conrey, J. B., 245 convolution, 17 convolution identity, 17, 18, 31 van der Corput, J. G., 32 counting function of a sequence, 43 of the primes, 1 of the squarefree integers, 42 Cram´ er, H., 30 Crandall, R., 34 critical line of the zeta function, 230 critical strip of the zeta function, 230 Cullen numbers, 102 Curtis, C. W., xiv esaro, E, 31 Daboussi, H., 179 Davenport, H., 30, 116, 143, 148, 149, 323 Cauchy-Davenport-Chowla thm., 141 Dedekind, J. W. R., 31, 99, 144 -Weber estimate, 285 completed zeta function, 257 conjecture, 302 zeta function, 256 Demichel, P., 323 density asymptotic, 43 Dirichlet, 88 logarithmic, 44 of squarefree integers, 43 of the primes, 1 Descartes, R., 31 Deshouilliers, J.-M., 148, 154 Deuring, M., 269 Diamond, H. G., xiv, 25, 29, 32, 179 Dickson, L. E. , xiv Diophantus of Alexandria, 111 Dirichlet, J. P. G. Lejeune, 37–39, 56, 99 approximation theorem, 138 character, 84 conductor of, 91 even, 109, 231 Gauss sum of, 89 imprimitive, 91 induced, 91 odd, 231 primitive, 91 quasiperiod of, 91 real, 109 class number formula, 270 convolution, 17 density, 88 divisor problem, 24, 32 formula, 25 hyperbola method, 25, 86
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