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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