4 papers
Shadow line distributions
Jennifer S. Balakrishnan, Mirela Çiperiani, Barry Mazur +1
Let be an elliptic curve over with Mordell--Weil rank and be an odd prime of good ordinary reduction. For every imaginary quadratic field satisfying th…
Selmer Ranks of Quadratic Twists of Elliptic Curves with Partial Rational Two-Torsion
Zev Klagsbrun
This paper investigates which integers can appear as 2-Selmer ranks within the quadratic twist family of an elliptic curve E defined over a number field K with E(K)[2] = Z/2Z. We s…
The spin of prime ideals
J. B. Friedlander, H. Iwaniec, B. Mazur +1
Fixing a nontrivial automorphism of a number field K, we associate to ideals in K an invariant (with values in {0,1,-1}) that we call the "spin" and for which the associated L-func…
Twisting commutative algebraic groups
B. Mazur, K. Rubin, A. Silverberg
If is a commutative algebraic group over a field , is a commutative ring that acts on , and is a finitely generated free -module with a right action of the abs…