366 Index
function
arithmetic, 3, 16
additive, 16
big-Omega, 16, 21
divisor, 16
Euler phi, 16
identity, 16
Liouville, 16
mean value of, 42
multiplicative, 16
obius mu, 18
partition, 104
radical, 16
small-omega, 16
sum-of-divisors, 17
totally additive, 16
totally multiplicative, 16
von Mangoldt, 2
Artin L-, 296
basis function, 68
Chebyshev psi, 2
Chebyshev theta, 2
class function, 76
completed Dedekind zeta, 257
completed Riemann zeta, 230
counting function, 43
of the primes, 1
of the squarefree integers, 42
Dedekind zeta, 256
Dirichlet L-function, 85
analytic continuation of, 162, 231
functional equation of, 231
elliptic, 248
entire function
canonical factorization of, 238
canonical product of, 238
exponent of convergence, 237
Hadamard factorization theorem,
238
of exponential type, 252
order of, 237
rank of, 238
gamma, 223–225
functional equation of, 224
logarithmic derivative, 275, 307
Gauss bracket, 2
generating, 63
indicator function, 43
integer part, 2
integral logarithm, 1
Jacobi theta, 216, 249
Lerch zeta, 251
Riemann Xi, 230
Riemann xi, 230
canonical factorization of, 240
order of, 240
Riemann zeta, 62, 63
analytic continuation of, 162, 229
critical line of, 230
critical strip of, 230
functional equation of, 229
nontrivial zeros of, 240
trivial zeros of, 230
sawtooth, 11
smoothed Chebyshev, 173, 307
summatory function, 3, 41, 158
of the divisor function, 23
of the Euler phi function, 21
of the logarithm, 3
of the obius function, 50
of the von Mangoldt function, 3
test, 315
functional equation
of Dirichlet L-functions, 231
of the Dedekind zeta function, 266
of the gamma function, 224
of the Jacobi theta function, 218
of the Riemann zeta function, 229
gamma factor, 231, 257
gamma function, 223–225
functional equation of, 224
logarithmic derivative of, 307
Gauss, J. K. F., 1, 18, 23, 27, 31, 99,
144
classical Gauss sum, 70
formula of, 275
Gauss bracket, 2
Gauss sum of a character, 89
Gegenbauer, L. B., 55
Gerono, G. C., 150
Goldbach, C., 108
binary problem, 28, 145
ternary problem, 145, 147, 155
Goldfeld, D. M., 194, 205
Goldston, D. A., 30
Gonek, S. M., 30
Gourdon, X., 323
Graham, S. W., 55
Gram, J. P., 55
Granville, A., 30, 55, 102
Green, B. J., 328
Gronwall, T. H., 205
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