Index 369 obius, A. F., 31 first inversion formula, 18 function, 18 second inversion formula, 19 Montgomery, H. L., xiv, 29, 30, 67, 102, 154, 223 Moore, E. H., 99 Mordell, L. J., 149, 269 Moroz, B. Z., 101 Mostert, M., 144 Mozzochi, C. J., 29, 32 Mukhopadhyay, M., 105 multiplicative arithmetic function, 16 Mumford, D., 223 Nagell, T., 83, 116 Narkiewicz, W., xiv neighborhood method, 41 Newman, D. J., 64, 287 Noether, A. E., 99 nome, 249 noneffectiveness in number theory, 194 nonprincipal character, 85 normal order, 46 method, 46 of log(d(n)), 49 of Ω(n), 48 of ω(n), 47 notation Bachmann big-O, 7 Hardy, 7 Landau small-o, 7 Vinogradov, 7 Oesterl´ e, J., 205 order of an arithmetic function average, 24 maximal, 21 minimal, 21 normal, 46 order of an entire function, 237 Page, A., 147, 205 Paley, R. E. A. C., 102 partial summation, 10 partition function, 104 Patterson, S. J., 102 perfect number, 38 periodization of a function, 214 Perron, O., 166 Perron formula, 160 Perrott, J., 33 Peter, F., 99 Piatetski-Shapiro, I. I., 101 Pil’tja ˘ G. Z., 30 Piltz, A., 103 Pintz, J., 29, 30 Plancherel, M. formula, 81, 82 PNT, 1 Poisson, S. D. multivariable summation formula, 215 summation formula, 214 de Polignac, A., 29 olya, G. -Vinogradov inequality, 93, 102 Pomerance, C. B., 30, 34 primary factor, 235 Prime Number Theorem, 1, 5, 10, 42, 170, 173 primitive character, 91 principal Dirichlet character, 85 principle maximum, 196 of inclusion and exclusion, 28 problem binary Goldbach, 28, 145 Dirichlet divisor, 24, 32 Riemann Hypothesis, 245 ternary Goldbach, 145, 147, 155 twin prime, 28, 101 Waring’s, 112, 148 Pythagorean triples, 111 Rademacher, H., 145 radical of an integer, 16 Ram Murty, M., 28 Ramanujan, S. A., 6, 31, 46, 55, 89, 179 Circle Method, 144 Ramanujan sum, 102 rank of an entire function, 238 Rankin, R. A., 28, 30, 55, 105 regulator of a number field, 267 relative error, 1 representation induced, 293 space, 71 RH, 245 Ricci, G., 30 Richert, H.-E., 55 te Riele, H., 154 Riemann, G. F. B., 166, 244 completed zeta function, 230 -Lebesgue Lemma, 180
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