Recent content by jian1

  1. J

    Decreasing sequence of subharmonic functions

    Homework Statement Let u(z) be a continuous function from D to [-inf, inf) (In the extended field sense which includes -inf). Suppose u_n (z) is a decreasing sequence of subharmonic functions on D such that u_n converges to a function v pointwisely. Show that v(z) is subharmonic. Homework...
  2. J

    Entire function and it's order

    never mind, I figured it out. :) thanx
  3. J

    Mittag-Leffler and weierstrass theorem

    say you have a function f(z) with all the desired poles, and another function g(z) with desired zeros, since both poles are zeros are distinct, a function f(z)g(z) will be a meromorphic function with both desired poles and zeros. Now the problem is that singular part(s) in f(z) is no longer...
  4. J

    Mittag-Leffler and weierstrass theorem

    Homework Statement Let G be a region and let {a_n} and {b_m} be two sequences of distinct points in G such that a_n != b_m for all n,m. Let S_n(z) be a singular part at a_n and let p_m be a positive integer. Show that there is a meromorphic function f on G whose only poles and zeros are...
  5. J

    Solve the algebraic equation,Galois group of FF, and prove/disprove.

    Please someone , these questions will be on the final examination and it'll take place tomorrow, none of us had got these questions so far... :(
  6. J

    Solve the algebraic equation,Galois group of FF, and prove/disprove.

    1. is to solve the equation, means to get the x, and I have no clue... 2.I think it's solvable, thus I used hensel lemma and got f'(x)=2x with |f(x)|_7... but haven't got a number which can satisfy the equation 3. for n+1, up to n^2 there will be n^2+1, and minus the n one in p^n, thus u...
  7. J

    Solve the algebraic equation,Galois group of FF, and prove/disprove.

    1. x^4+2x^3+3x^2+4x+5=0 2. is the equation x^2=2 solvable in 7-adic numbers? 3. find the group Gal(F_p^n^2/ F_p^n), I got n^2-n+1... is it right?
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