Katharina Muller

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20242026

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math.NT2026

A new perspective on the rank of Mazur's Eisenstein Hecke algebra

Jaclyn Lang, Katharina Müller, Bharathwaj Palvannan

Let $N, p \geq 5$ be primes such that $N \equiv 1 mod p$ . We study the rank $r$ of the Hecke algebra that parametrizes modular forms of weight 2 and level $N$ that are Eisenstein…

math.NT2026

Bowen--Franks groups and minus class groups of cyclotomic number fields with prime conductor

Antonio Lei, Katharina Müller, Daniel Vallières

Let $p$ be an odd rational prime and consider the cyclotomic number field $K = Q (ζ_{p})$ of conductor $p$ . We construct a directed graph $Y$ on $p - 1$ vertices for which th…

math.NT2026

Iwasawa theory for abelian towers of digraphs

Antonio Lei, Katharina Müller

Let $p$ and $ℓ$ be prime numbers, and $d \geq 1$ an integer. We formulate and prove Iwasawa main conjectures of the Picard groups and Bowen--Franks groups in $Z_{p}^{d}$ -tower…

math.NT2025

Isogeny graphs with level structures arrising from the Verschiebung map

Antonio Lei, Katharina Müller

We enhance an isogeny graph of elliptic curves by incorporating level structures defined by bases of the kernels of iterates of the Verschiebung map. We extend several previous res…

math.NT2025

On $Z_{p}$ -towers of graph coverings arising from a constant voltage assignment

Antonio Lei, Katharina Müller

We investigate properties of $Z_{p}$ -towers of graph coverings that arise from a constant voltage assignment. We prove the existence and uniqueness (up to isomorphisms) of s…

math.NT2024

Hilbert's tenth problem for families of $Z_{p}$ -extensions of imaginary quadratic fields

Katharina Müller, Anwesh Ray

Via a novel application of Iwasawa theory, we study Hilbert's tenth problem for number fields occurring in $Z_{p}$ -towers of imaginary quadratic fields $K$ . For a odd prime…

A new perspective on the rank of Mazur's Eisenstein Hecke algebra

Bowen--Franks groups and minus class groups of cyclotomic number fields with prime conductor

Iwasawa theory for abelian towers of digraphs

Isogeny graphs with level structures arrising from the Verschiebung map

On Zp​-towers of graph coverings arising from a constant voltage assignment

Hilbert's tenth problem for families of Zp​-extensions of imaginary quadratic fields

On $Z_{p}$ -towers of graph coverings arising from a constant voltage assignment

Hilbert's tenth problem for families of $Z_{p}$ -extensions of imaginary quadratic fields