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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