Loading [MathJax]/jax/output/HTML-CSS/jax.js

Andrew Granville's Home Page

2003 Publications

The number of fields generated by the square root of values of a given polynomial (with Pam Cutter and Tom Tucker)
Canadian Mathematical Bulletin, 46 (2003), 71-79.

The abc-conjecture is applied to various questions involving the number of distinct fields Q(f(n)), as one varies over integers n.

Article

Decay of mean-values of multiplicative functions (with K. Soundararajan)
Canadian Journal of Mathematics, 55 (2003), 1191-1230.

We give an explicit version of Halasz's Theorem, giving an upper bound on the mean value of multiplicative functions in terms of its "distance" from any function of the form nit. We give examples to show our bounds are best possible within a factor of 10.

Article

Distribution of values of L(1,χd) (with K. Soundararajan)
Geometric and Functional Analysis, 13 (2003), 992-1028; (Errata) 14 (2003), 245-246.

We prove various results (including some conjectures of Montgomery and Vaughan) on the distribution of the values of L(1,χd), including finding complex moments and extreme values.

Article