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
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