Unformatted text preview: interesting observations about number ﬁelds of small discriminant, be sure to share them. 3. (5 points) Compute the class group of Q ( √33). 4. (5 points) Compute the class group of Q ( √163). 5. (5 points) Compute the class group of Q ( √14). 6. (5 points) Compute the class group of Q (7 1 / 3 ). 7. (8 points) Compute the class group of Q ( √ α ), where α 3α7 = 0. 8. (8 points) Compute the class group of Q ( ζ 11 ). 9. (*, 12 points) Prove that the class number of Q ( √13947137572). Hints: No, the Ankeny and Chowla result doesn’t apply. Use Dirichlet’s class number formula, in combination with a computer and some analytic number theory. But just asking PARI or SAGE what the class number is (it’s 17852) is cheating....
View
Full Document
 Spring '13
 FrankThorne
 Algebra, Number Theory, Algebraic number theory, Class Group, Frank Thorne, John Voight

Click to edit the document details