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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

4 votes
Accepted

Tate uniformization of nonsplit semistable elliptic curves

A form of this is contained in Silverman, second book, Chapter V, Corollary 5.4. I guess that the image of Gm' in E (at the level of Q_p-points) may have index 2.
moonface's user avatar
  • 748
9 votes

Is there a simple way to compute the number of ways to write a positive integer as the sum o...

See Granville-Soundararajan, ``The distribution of values of L(1, \chi),'' for (whatever is known about) the distribution of r_3(n)/sqrt(n).
moonface's user avatar
  • 748
2 votes

Does MAGMA have a function to decide if two indefinite, integral quadratic forms are isometric?

not an answer to the question, but: Checking isometry is much easier for indefinite forms; it's purely local, by strong approximation for the spin group. If interested search for "spinor genus."
moonface's user avatar
  • 748