Frobenius distributions : Lang-Trotter and Sato-Tate conjectures / [edited by] David Kohel and Igor Shparlinski.

Includes bibliographical references.

* 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

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.