Adam Logan

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math.NT2024

Rings of Hilbert modular forms, computations on Hilbert modular surfaces, and the Oda-Hamahata conjecture

Adam Logan

The modularity of an elliptic curve $E / Q$ can be expressed either as an analytic statement that the $L$ -function is the Mellin transform of a modular form, or as a geometri…

math.NT2024

The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space

Taylor Dupuy, Anton Hilado, Colin Ingalls +1

Let $K$ be a $Q$ -Clifford algebra associated to an $(n - 1)$ -ary positive definite quadratic form and let $O$ be a maximal order in $K$ . A Clifford-Bianchi group i…

math.NT2023

The automorphisms of certain Kummer surfaces act on the points mod $p$ by the alternating group

Adam Logan, Owen Patashnick

For the family of Kummer surfaces of the square of an elliptic curve over the prime field $F_{p}$ with $p$ odd, we show that if the automorphism group acts transitively on t…

Rings of Hilbert modular forms, computations on Hilbert modular surfaces, and the Oda-Hamahata conjecture

The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space

The automorphisms of certain Kummer surfaces act on the points mod p by the alternating group

The automorphisms of certain Kummer surfaces act on the points mod $p$ by the alternating group