... You may write to me if you have questions. ... Let G be a locally compact abelian group, H be a compact open subgroup, and let f L1 (G). Fix a Haar measure µ on G to define the Fourier transform f : G C. a) If f (g ) = 0 for all g H , show f : G C is constant on H -cosets in G: f ( ) = f () if H . ... Let p be a prime. p 1 |y |2 1+1/p p a) In the topological group R в Qp , show Z (embedded diagonally) is discrete but not co-compact and Z[1/p] (embedded diagonally) is both discrete and cocompact. ...