Frobenius Distributions:: Lang-Trotter and Sato-Tate Conjectures
About this Title
David Kohel, Aix Marseille Université, Marseille, France and Igor Shparlinski, University of New South Wales, Sydney, Australia, Editors
Publication: Contemporary Mathematics
Publication Year 2016: Volume 663
ISBNs: 978-1-4704-1947-9 (print); 978-1-4704-3003-0 (online)
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 Mathématiques, 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.
Graduate students and research mathematicians interested in computational aspects of number theory and the interplay between number theory and algebraic geometry.
Table of Contents
- Jean-Pierre Serre – Lettre à Armand Borel
- Grzegorz Banaszak and Kiran S. Kedlaya – Motivic Serre group, algebraic Sato-Tate group and Sato-Tate conjecture
- Alina Bucur and Kiran S. Kedlaya – An application of the effective Sato-Tate conjecture
- Francesc Fité, Kiran S. Kedlaya and Andrew V. Sutherland – Sato-Tate groups of some weight 3 motives
- Francesc Fité and Andrew V. Sutherland – Sato-Tate groups of $y^2=x^8+c$ and $y^2=x^7-cx$.
- David Harvey and Andrew V. Sutherland – Computing Hasse–Witt matrices of hyperelliptic curves in average polynomial time, II
- Everett W. Howe – Quickly constructing curves of genus $4$ with many points
- Kevin James – Variants of the Sato-Tate and Lang-Trotter Conjectures
- Gilles Lachaud – On the distribution of the trace in the unitary symplectic group and the distribution of Frobenius
- Blake Mackall, Steven J. Miller, Christina Rapti and Karl Winsor – Lower-Order Biases in Elliptic Curve Fourier Coefficients in Families