Index 371 Prime Number Theorem, 1, 2, 5, 10, 42, 159, 170, 173 Schur orthogonality, 75 Schur’s Lemma, 74 second mean value, 35 Siegel, 193 Siegel-Walfisz, 204 uniqueness of Dirichlet series, 67 theta function, 216, 249 theta-constant, 219, 249 Titchmarsh, E. C., 67, 177, 178 totally additive function, 16 totally multiplicative function, 16 Touchard, J., 38 transform finite Fourier, 69 Fourier, 8, 213 Fourier transform on a group, 79 Mellin, 227, 251, 315 Trifonov, O., 55 trigonometric basis functions, 209 trivial group character, 76 trivial zeros of the zeta function, 230 truncated explicit formula, 310 Tur´ an, P., 43, 46, 55 twin prime problem, 28, 101 uniformity of estimates, 7 unit disk, 206 unordered sum or product, 59 upper half plane, 216 de la Vall´ ee Poussin, C. G. J. N., 1, 159, 177 valuation, 247 Vaughan, R. C., 30, 102, 143, 148, 155 Vinogradov, I. M., 103, 143, 146, 155, 178 notation, 7 olya-Vinogradov inequality, 93, 102 Voronin, S. M., 323 Voronoi, G. F., 32 Walfisz, A. Z., 55, 147 Siegel-Walfisz theorem, 204 Waring, E. Hilbert-Waring theorem, 143 Waring’s Problem, 112, 148 Warning, E. Chevalley-Warning theorem, 151 Weber, H. M., 99, 100 Dedekind-Weber estimate, 285 Weierstrass, K. T. W., 252 primary factor, 235 Weil, A., 144, 315 Weiss, G. M., 216 Westzynthius, E., 30 Weyl, H. K. H., 99, 145, 147 Weyl differencing, 132 Weyl sum, 130 Weyl’s inequality, 132 Whaples, G. W. Artin-Whaples product formula, 247 Wieferich, A., 148 Wielandt, H., 224 Wigert, S., 31 Williams, K. S., xiv Wintner, A. F., 43 Wooley, T. D., 112, 149 Wright, E. M., xiv Wu, J., 101 Yao, Q., 29 Yıldırım, C. Y., 30 Zagier, D., 205 Zeitz, H., 30 zeta function Dedekind, 256 Lerch, 251 Riemann, 62 Zhang, Y., 30 Zinoviev, D., 154 Zygmund, A. S., 216
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