Cruz Castillo

collaborators

3 papers

math.NT2026

Non-vanishing for quartic Hecke $L$ -functions and ranks of elliptic curves

Cruz Castillo, Alexandre de Faveri, Alexander Dunn

We show that a positive proportion of Hecke $L$ -functions attached to the quartic residue symbols $(\frac{\cdot}{q})_{4}$ for squarefree $q \in Z [i]$ do not vanish…

math.NT2025

Arithmetic properties of generalized Frobenius partitions

Scott Ahlgren, Cruz Castillo

Ramanujan proved three famous congruences for the partition function modulo 5, 7, and 11. The first author and Boylan proved that these congruences are the only ones of this type.…

math.NT2025

Eisenstein series modulo prime powers

Scott Ahlgren, Cruz Castillo, Clayton Williams

If $p \geq 5$ is prime and $k \geq 4$ is an even integer with $(p - 1) ∤ k$ we consider the Eisenstein series $G_{k}$ on $SL_{2} (Z)$ modulo powers of $p$ . It is…

Non-vanishing for quartic Hecke L-functions and ranks of elliptic curves

Arithmetic properties of generalized Frobenius partitions

Eisenstein series modulo prime powers

Non-vanishing for quartic Hecke $L$ -functions and ranks of elliptic curves