Abel Castillo

activity

20132016

most citedBounded gaps between primes in number fields and function fields

4 citations · 6 across the 4 of their papers we have counts for

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math.NT2016

The normal order of of the divisor-counting function for invariants of rank 2 Drinfeld modules

Abel Castillo

We compute the first and second moments of the divisor-counting function for the Euler-Poincaré characteristic and the trace of Frobenius for the reductions modulo $p$ of a rank 2…

math.NT2016

Distribution of the trace of Frobenius on average for rank 2 Drinfeld modules

Abel Castillo

Let $q$ be an odd prime power, $a \in F_{q} [T]$ and $u \in F_{q}^{*}$ . Provided $q \geq 17$ , we compute the average number of primes $p$ for which the characteristic po…

math.NT2016

On Hilbert's irreducibility theorem

Abel Castillo, Rainer Dietmann

In this paper we obtain new quantitative forms of Hilbert's Irreducibility Theorem. In particular, we show that if $f (X, T_{1}, \dots, T_{s})$ is an irreducible polynomial with intege…

math.NT2014★ 4 cited

Bounded gaps between primes in number fields and function fields

Abel Castillo, Chris Hall, Robert J. Lemke Oliver +2

The Hardy--Littlewood prime $k$ -tuples conjecture has long been thought to be completely unapproachable with current methods. While this sadly remains true, startling breakthroughs…

math.NT2013★ 2 cited

Congruences for Ramanujan's f and ω functions via generalized Borcherds products

Jen Berg, Abel Castillo, Robert Grizzard +3

Bruinier and Ono recently developed the theory of generalized Borcherds products, which uses coefficients of certain Maass forms as exponents in infinite product expansions of mero…