Index 365
interchange, 23
inverse, 18
L-function, 85
functional equation of, 231
primes in arithmetic progressions, 100
ring, 17
series, 63, 64, 157
convergence, 65
formal, 63
line of absolute convergence, 66
line of convergence, 65
uniform convergence, 65
uniqueness theorem, 67
theorem of, 83
unit theorem, 264
discriminant of a number field, 277
divisor
block divisor, 36
function, 16
Hall divisor, 36
Dress, F., 148
Edwards, H. M., xiv
Effinger, G., 154
Elliott, P. D. T. A., 43
elliptic function, 248
Encke, J. F. F., 27
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
equation
Diophantine, 111
Eratosthenes of Cyrene, 27
Erd¨ os, P., 29, 30, 34, 43, 58, 178
-Kac theorem, 48
Estermann, T., 55
Euclid of Alexandria, 111
Euler, L., 108, 225
-Maclaurin summation, 12, 31
-Mascheroni constant, 12, 15
phi function, 16
product formula, 60, 62, 85, 99
Evans, R. J., xiv
Everett, C. J., 64, 99
exceptional conductor, 193
explicit formula
Guinand-Weil, 316
von Mangoldt, 307
exponent of convergence, 237
exponential type, 252
de Fermat, P.
Fermat numbers, 108
method of infinite descent, 112
Filaseta, M. A., 55
finite Fourier expansion, 68
finiteness of the class number, 266
First Frobenius orthogonality thm., 77
first mean value theorem, 35
Fogels, E., 55
form
diagonal, 113
formal Dirichlet series, 63
formal power series, 63
formula
analytic class number, 267
Dirichlet class number, 270
Dirichlet’s, 25
Eratosthenes-Legendre sieve, 28
Euler product, 60, 62, 85
Euler-Maclaurin summation, 12, 36
first obius inversion, 18
Guinand-Weil explicit, 316
Jensen’s, 236
Meissel’s, 23, 25
Mertens’, 15
partial summation, 10
Perron, 160
Plancherel, 81, 82
second obius inversion, 19
Selberg, 178
Stirling’s, 12, 309
von Mangoldt explicit, 307, 310
Fourier coefficients, 210
Fourier series, 210
convergence of, 212
Fourier transform, 213, 215
inverse, 79
inversion theorem, 79, 82
on a finite group, 79
Plancherel formula, 81, 82
Fouvry, E., 30
Franel, J., 32
Freeman, D. E., 143
Friedlander, J. B., 28, 101, 196
Frobenius, F. G., 99
first orthogonality theorem, 77
reciprocity theorem, 295
second orthogonality theorem, 107
Previous Page Next Page