Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication

INDEX

A

Abatzoglou, A., 346

Abel, N. H., 79, 219

Abelian extension, see Field, extension

adele, 5, 317–318

Affine space, 284

Algebraic groups, 115

Algebraic integers, 3, 78, 88

Apostol, T., 205, 210, 335

Approximation Theorem, 331

Arndt, F., 64

Artin, E., 166, 290, 335

Artin map, 97–98, 107, 109–112, 114, 144–148, 150, 152, 154–155, 163, 164, 172, 218

idelic, 156–157, 312, 322, 326

Artin Reciprocity Theorem, see Class field theory, Artin Reciprocity Theorem

Artin symbol, 95–97, 106, 111, 145–146, 150, 153, 155, 171. See also Artin map

relation to Legendre symbol, 96, 106, 150

Associate, 6, 68

Atkin, A. O. L., 297, 303–304, 343

B

Bachmann, P., 57

Baker, A., 4, 135, 226, 247, 335

Belding, J. V., 345

Berndt, B. C., 79, 261, 343, 345

Berwick, W. E. H., 247, 335

Biermann, K. R., 335

Biquadratic reciprocity, see Reciprocity, biquadratic

Birch, B. J., 227, 240, 247, 335

Borevich, Z. I., 53, 88, 90, 93, 119, 129, 134, 335

Borwein, J. M., 196, 336

Borwein, P. B., 196, 336

Briggs, W. E., 172, 336

Brillhart, J., 297, 343

Bröker, R., 345

Bruckner, G., 172, 174, 336

Buell, D. A., 27, 336, 345

Bühler, W. K., 57, 336

Burde, K., 345

Burkhardt, J. J., 9, 336

Bussotti, P., 9, 343

C

Calculus of finite differences, 11, 19

Cassou–Noguès, P., 220, 297, 336

Čebotarev Density Theorem, 4, 144, 152–155, 160, 162, 171, 176

Chan, H. H., 346

Chandrasekharan, K., 187, 252, 336

Character:

assigned, 49–50, 52, 62–63, 113

biquadratic, 75

complete, 52

group, 52

Chinese Remainder Theorem, 37, 41, 50, 142, 324, ...