368 Index von Koch, N. F. H., 314 Kolesnik, G. A., 32, 55 Kolmogorov, A. N., 210 De Koninck, J.-M., 45 Korevaar, J., 287 Korobov, N. M., 178 Kowalski, E., 67, 223 Kronecker, L., 32, 99, 103 theorem of, 267 Kubilius, J., 43 Kummer, E. E., 102 L-function Artin, 297 completed Dirichlet, 231 Dirichlet, 85 Lagrange, J. L., 145, 148, 150 Lambert, J. H., 31, 104 Landau, E. G. H., 31, 32, 55, 102, 148, 165, 182, 205, 246 -Siegel zeros, 193 Bohr-Landau theorem, 323 Prime Ideal Theorem, 281 small-o notation, 7 theorem of, 157, 190 trick, 6 Landsberg, G -Schaar formula, 219 lattice points under a hyperbola, 25 Law of Quadratic Reciprocity, 222 least positive quadratic nonresidue, 94 Lebesgue, H. L. Riemann-Lebesgue Lemma, 180 Lebesgue, V. A., 108 Legendre, A.-M., 27 Law of Quadratic Reciprocity, 100 Legendre identity, 2 sieve formula, 28 symbol, 70 lemma Borel-Carath´ eodory, 197 Hua’s, 135 Riemann-Lebesgue, 180 Schur’s, 74 Lerch, M. zeta function, 251 Levinson, N., 245 Lewis, D. J., 149 Libri, G., 144 limit inferior and superior, 4 Linnik, Y. V., 148 Lionnet, F. J. E., 182 Liouville, J., 16, 31, 150 Lipschitz, R. O. S., 102, 247 summation formula, 251 Littlewood, J. E., 144, 177 Circle Method, 145 local average, 23 local factor, 296 logarithmic density, 44 Lou, S. T., 29 Luca, F., 45, 105 Maccioni Ruju, P. A., 144 Maclaurin, C., 12, 31 Maier, H., 30 major arcs, 117 Mandelbrojt, S., 99 von Mangoldt, H. C. F., 2, 55, 245, 246 explicit formula, 307, 310 Mascheroni, L., 12, 15 Maschke, H., 99 complete reducibility theorem, 73 Matiyasevich, Y. V., 111 matrix entries of a representation, 74 maximal order, 21 Maximum Principle, 196 Maynard, J., 30 mean value, 42 Meissel, D. F. E., 23, 25, 32, 55 Mellin transform identity, 266 Mellin, R. H., 166 inversion theorem, 251 transform, 227, 251, 315 Mend` es France, M., 179 Merlin, J., 28, 150 Mersenne, M., 31, 101 Mertens, F. C. J., 10, 13, 21, 31, 83, 100, 177 Mertens’ formula, 15 method circle, 117 Dirichlet hyperbola, 25, 53 neighborhood, 41, 158 normal order, 46 of Chebyshev, 3, 17, 19 of contour integrals, 158 of partial summation, 10 Meyer, A., 100 minimal order, 21 Minkowski, H. theorem of, 279 minor arcs, 117
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