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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