Katharina Müller

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math.NT2026

Iwasawa theory of (directe) Cayley graphs

Debanjana Kundu, Katharina Müller, Alexis newton +2

In this article, we prove the Defect Conjecture for Cayley graphs of abelian groups, dihedral groups, and groups of the form $\mathbb{Z}/p\mathbb{Z} \rtimes \mathbb{Z}/(p-1)\mathbb…

math.NT2023

On towers of Isogeny graphs with full level structure

Antonio Lei, Katharina Müller

Let $p, q, l$ be three distinct prime numbers and let $N$ be a positive integer coprime to $pq l$ . For an integer $n \geq 0$ , we define the directed graph $X_{l}^{q} (p^{n} N)$ whose vertices a…

math.NT2023

On the non-commutative Iwasawa main conjecture for voltage covers of graphs

Sören Kleine, Katharina Müller

Let $p$ be a rational prime, and let $X$ be a connected finite graph. In this article we study voltage covers $X_{\infty}$ of $X$ attached to a voltage assignment $α$ which takes val…

math.NT2023

On the Zeta functions of supersingular isogeny graphs and modular curves

Antonio Lei, Katharina Müller

Let $p$ and $q$ be distinct prime numbers, with $q \equiv 1 (mod 12)$ . Let $N$ be a positive integer that is coprime to $pq$ . We prove a formula relating the Hasse--Weil zeta functi…

math.NT2023

On ordinary isogeny graphs with level structure

Antonio Lei, Katharina Müller

Let $l$ and $p$ be two distinct prime numbers. We study $l$ -isogeny graphs of ordinary elliptic curves defined over a finite field of characteristic $p$ , together with a level stru…