9 citations · 13 across the 3 of their papers we have counts for
5 papers · 1 filter
Galois representations attached to Q-curves and the generalized Fermat equation A^4 + B^2 = C^p
Jordan S. Ellenberg
We show that the mod p Galois representations attached to a Q-curve E of degree d over an imaginary quadratic number field K are surjective for all p larger than some constant M_{K…
On the error term in Duke's estimate for the average special value of L-functions
Jordan S. Ellenberg
Let F be an orthonormal basis of weight 2 cusp forms on Gamma_0(N). We show that various weighted averages of special values L(f \tensor chi, 1) over f in F are equal to 4 pi + O(N…
The number of extensions of a number field with fixed degree and bounded discriminant
Jordan S. Ellenberg, Akshay Venkatesh
We give an upper bound on the number of extensions of a fixed number field of prescribed degree and discriminant less than X; these bounds improve on work of Schmidt. We also prove…
Serre's conjecture over F_9
Jordan S. Ellenberg
In this paper, we show that an odd Galois representation rhobar: Gal(Qbar/Q) --> GL_2(F_9) satisfying certain local conditions at 3 and 5 is modular. Our main tool is an idea of Ta…
Congruence ABC implies ABC
Jordan S. Ellenberg
The ABC conjecture of Masser and Oesterle' states that if (a,b,c) are coprime integers with a + b + c = 0, then sup(|a|,|b|,|c|) < c_e (rad(abc))^{1+e} for any e > 0. Oesterle' has…