|322 TMCB |
Department of Mathematics
Brigham Young University
Provo, UT 84602
S4 and S~4 extensions of Q ramified at only one prime
Journal of Number Theory, 75 (1999), pp. 185-197.
For each prime p in a certain family of odd primes, we construct an S4 extension of Q unramified outside p. We show that for all p congruent to 3 modulo 8 in our family, this S4 extension embeds in an S~4 extension, which is also unramified outside p. Invoking Serre's conjecture (in a proven case) allows us to relate the splitting of primes in these extensions to certain modular forms of level 1.
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