5 papers
An entire function that violates quasiminimality
Spencer Dembner
Zilber's celebrated quasiminimality conjecture states that a subset of defined by polynomials and exponentials is either countable, or has countable complement. Koiran…
Complex curves in o-minimal geometry
Spencer Dembner
There has recently been considerable progress relating o-minimality to complex analytic geometry. Yet almost nothing is known about coherent cohomology or the classification of vec…
Algebraic and o-minimal flows beyond the cocompact case
Spencer Dembner, Hunter Spink
Let be an algebraic variety, and let be a discrete subgroup whose real and complex spans agree. We describe the topological closure…
A Note on Congruences for Weakly Holomorphic Modular Forms
Spencer Dembner, Vanshika Jain
Let be the ring of integers of a number field . Write , and suppose that $$f(z) = \sum_{n \gg - \infty}^{\infty} a_f(n) q^n \in M_{k}^{!}(\operatorname{SL}…
Hyperelliptic Curves and Newform Coefficients
Spencer Dembner, Vanshika Jain
We study which integers are admissible as Fourier coefficients of even integer weight newforms. In the specific case of the tau-function, we show that for all odd primes $\ell < 10…