The Benefits of an Alternative Approach to Analytic Number Theory

In our talk we will survey the alternative (or “pretentious”) approach to analytic number theory, which has the potential to be more flexible and broad reaching than traditional zeta-function methods, highlighting some spectacular recent developments. In this “sampler” we give some indication of the change in perspective that motivates this shift in techniqu

The Personal and Professional Characteristics of Master Therapists and Matched Controls

This dissertation is an attempt to replicate the results of a study conducted by Len Jennings(1996) which provided the data underlying the cognitive, emotional, and relational (CER) model of therapist excellence. As outlined in Jennings\u27(1996) research protocol, data were gathered through semi-structured interviews with ten master therapists chosen through a snowball sampling technique. Unlike the original study, this dissertation includes a matched control group intended to provide insight about the generalizability of the categories/domains of CER

Mean values of multiplicative functions over function fields

We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical difficulties that arise over the integers disappear in the function field setting, which helps bring out more clearly the main ideas of the proofs over number fields. We also obtain Lipschitz estimates showing the slow variation of mean values of multiplicative functions over function fields, which display some features that are not present in the integer situation

Gaps between fractional parts, and additive combinatorics

We give bounds on the number of distinct differences Na - a as a varies over all elements of a given finite set A ⊆ (ℝ/ℤ), d ≥ 1 and Na is a nearest neighbour to a

Big Biases Amongst Products of Two Primes

We show that substantially more than a quarter of the odd integers of the form pqpq up to xx, with p,qp,q both prime, satisfy p≡q≡3 (mod4)p≡q≡3 (mod4)

On multiplicative functions which are small on average

Let $f$ be a completely multiplicative function that assumes values inside the unit disc. We show that if \sum_{n2, for some $A>2$, then either $f(p)$ is small on average or $f$ pretends to be $\mu(n)n^{it}$ for some $t$.Comment: 51 pages. Slightly strengthened Theorem 1.2 and simplified its statement. Removed Remark 1.3. Other minor changes and corrections. To appear in Geom. Funct. Ana