Allysa Lumley

Let $a,q$ be relatively prime integers. Then consider $$ \psi (x; q, a) = \sum_{ \begin{smallmatrix} n \le x \\ {n \equiv a} \ (\mathrm{mod}\, {q}) \end{smallmatrix} } \Lambda(n) .$$We discuss new explicit bounds for $\psi(x; q, a)$, which provide an...

Let q≡1(mod4) be a prime power and Fq be the finite field with q elements. Let 1/2σ1 be fixed. We consider D a monic square-free polynomial in Fq[T] and χD the Kronecker symbol associated with D. In this talk, we will discuss the distribution of...

We formulate, using heuristic reasoning, precise conjectures for the range of the number of primes in intervals of length yy around xx, where y≪(logx)^2y≪(log⁡x)^2. In particular, we conjecture that the maximum grows surprisingly slowly as yy ranges...