April 2013
Intermediate to advanced
384 pages
10h 3m
English
book
Primes of the Form x2+ny2: Fermat, Class Field Theory, and Complex Multiplication
by David A. Cox
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ADDITIONAL REFERENCES
A. References Added to the Text
A1. A. O. L. Atkin and F. Morain, Elliptic curves and primality proving, Math. Comp. 61 (1993), pp. 29–68.
A2. B. C. Berndt, Ramanujan's Notebooks, Part IV, Springer-Verlag, New York, 1994.
A3. B. C. Berndt, R. Evans and K. S. Williams, Gauss and Jacobi Sums, Wiley, New York, 1998.
A4. J. Brillhart and P. Morton, Class numbers of quadratic fields, Hasse invariants of elliptic curves, and the supersingular polynomial, J. Number Theory 106 (2004), pp. 79–111.
A5. P. Bussotti, From Fermat to Gauss: Infinite Descent and Methods of Reduction in Number Theory, Dr. Erwin Rauner Verlag, Augsburg, 2006.
A6. B. Cho, Primes of the form x2 + ny2 with conditions x ≡ 1 mod N, y ≡ 0 mod N, J. Number Theory 130 (2010), pp. 852–861.
A7. D. Cox, Galois Theory, 2nd edition, Wiley, Hoboken, New Jersey, 2012.
A8. D. Cox, J. McKay and P. Stevenhagen, Principal moduli and class fields, Bull. London Math. Soc. 26 (2004), pp. 3–12.
A9. W. Duke, Continued fractions and modular functions, Bull. Amer. Math. Soc. 42 (2005), pp. 137–162.
A10. A. Gee, Class fields by Shimura reciprocity, J. Théor. Nombres Bordeaux 11 (1999), pp. 45–72.
A11. A. Gee and P. Stevenhagen, Generating class fields using Shimura reciprocity, in Algorithmic Number Theory (Portland, OR, 1998), Lecture Notes in Comput. Sci. 1423, Springer-Verlag, Berlin, 1998, pp. 441–453.
A12. B. Gross, An elliptic curve test for Mersenne primes, J. Number Theory 110 (2005), pp. 114–119.
A13. F. Hajir ...
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.