Directions in Number Theory, 1st ed. 2016 Proceedings of the 2014 WIN3 Workshop Association for Women in Mathematics Series, Vol. 3

Exploring the interplay between deep theory and intricate computation, this volume is a compilation of research and survey papers in number theory, written by members of the Women In Numbers (WIN) network, principally by the collaborative research groups formed at Women In Numbers 3, a conference at the Banff International Research Station in Banff, Alberta, on April 21-25, 2014. The papers span a wide range of research areas: arithmetic geometry; analytic number theory; algebraic number theory; and applications to coding and cryptography.

The WIN conference series began in 2008, with the aim of strengthening the research careers of female number theorists. The series introduced a novel research-mentorship model: women at all career stages, from graduate students to senior members of the community, joined forces to work in focused research groups on cutting-edge projects designed and led by experienced researchers. The goals for Women In Numbers 3 were to establish ambitious new collaborations between women in number theory, to train junior participants about topics of current importance, and to continue to build a vibrant community of women in number theory. Forty-two women attended the WIN3 workshop, including 15 senior and mid-level faculty, 15 junior faculty and postdocs, and 12 graduate students.

Preface.- Insufficiency of the Brauer-Manin obstruction for rational points on Enriques surfaces (Balestrieri et al).- Shadow lines in the arithmetic of elliptic curves (Balakrishnan et al).- Galois action on the homology of Fermat curves (Davis et al).- Zeta functions of a class of Artin-Schreier curves with many automorphisms over finite fields (Bouw et al).- Hypergeometric series, truncated hypergeometric series, and Gaussian hypergeometric functions (Deines et al).- A generalization of S. Zhang's local Gross-Zagier formula for GL(2) (Maurischat).- p-adic q-expansion principles on unitary Shimura varieties (Caraiani et al).- Kneser-Hecke-operators for codes over finite chain rings (Feaver et al).- Ring-LWE cryptography for the number theorist (Elias et al).- Asymptotics for number fields and class groups (Wood).