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 $$\mathbb Q(\sqrt{f(n)})$$, 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 $$n^{it}$$. We give examples to show our bounds are best possible within a factor of 10.

Article

Distribution of values of $$L(1,\chi_d)$$ (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 $$L(1,\chi_d)$$, including finding complex moments and extreme values.

Article