Frobenius distributions : Lang-Trotter and Sato-Tate conjectures - Winter School on Frobenius Distributions on Curves (Marseille, France 17-21 Feb 2014); Kohel, David; Shparlinski, Igor; Workshop on Frobenius Distributions on Curves (Marseille, France 24-28 Feb 2014) (Providence : American Mathematical Society, 2016)
This volume contains the proceedings of the Winter School and Workshop on Frobenius Distributions on Curves, held from February 17-21, 2014 and February 24-28, 2014, at the Centre International de Rencontres Mathematiques, Marseille, France. This volume gives a representative sample of current research and developments in the rapidly developing areas of Frobenius distributions. This is mostly driven by two famous conjectures: the Sato-Tate conjecture, which has been recently proved for elliptic curves by L. Clozel, M. Harris and R. Taylor, and the Lang-Trotter conjecture, which is still widely open. Investigations in this area are based on a fine mix of algebraic, analytic and computational techniques, and the papers contained in this volume give a balanced picture of these approaches.
* Lettre a Armand Borel by J-P. Serre* Motivic Serre group, algebraic Sato-Tate group and Sato-Tate conjecture by G. Banaszak and K. S. Kedlaya* An application of the effective Sato-Tate conjecture by A. Bucur and K. S. Kedlaya* Sato-Tate groups of some weight 3 motives by F. Fite, K. S. Kedlaya, and A. V. Sutherland* Sato-Tate groups of $y^2=x^8+c$ and $y^2=x^7-cx$ by F. Fite and A. V. Sutherland* Computing Hasse-Witt matrices of hyperelliptic curves in average polynomial time, II by D. Harvey and A. V. Sutherland* Quickly constructing curves of genus 4 with many points by E. W. Howe* Variants of the Sato-Tate and Lang-Trotter conjectures by K. James* On the distribution of the trace in the unitary symplectic group and the distribution of Frobenius by G. Lachaud* Lower-order biases in elliptic curve Fourier coefficients in families by B. Mackall, S. J. Miller, c. Rapti, and K. Winsor
Includes bibliographical references.
Keywords: Frobenius algebras -- Congresses; Algebraic curves -- Congresses