18.785F16 Number Theory I Assignments: Problem Set 9

18.785F16 Number Theory I Assignments: Problem Set 8

18.785F16 Number Theory I Assignments: Problem Set 10

(a) Prove that for each integer n > 1 there are infinitely many (Z/nZ)-extensions of Q ramified at only one prime. (b) Prove that for each integer n > 2 there are no (Z/nZ)2-extensions of Q ramified at only one prime. Why does this not contradict the fact that (Z/pZ)2-extensions of Qp exists for every p? (c) Given an explicit example of a (Z/2Z)2-extension of Q ramified at only one prime (with ...

18.785F16 Number Theory I Lecture 18 Notes: Dirichlet L-functions, Primes in Arithmetic Progressions

18.785F17 Number Theory I Assignments: Problem Set 8

18.785F17 Number Theory I Assignments: Problem Set 9

These problems are related to the material covered in Lectures 17–19. Your solutions are to be written up in latex (you can use the latex source for the problem set as a template) and submitted as a pdf-file via e-mail to Collaboration is permitted/encouraged, but you must identify your collaborators, and any references you consulted. If therearenone,write“Sources consulted: none”atthetopofyour...