M. Larsen

activity

20242026

collaborators

9 papers

math.NT2026

Robust additive bases without minimal subbases

Daniel Larsen, Michael Larsen

There exists a set $A$ of positive integers such that the number of representations of a large positive integer $m$ as a sum of two elements of $A$ grows with a lower bound of orde…

math.RT2025

Tensor Power Asymptotics for Linearly Reductive Groups

Michael J. Larsen

Given a finite-dimensional faithful representation $V$ of a linearly reductive group $G$ over a field $K = K ˉ$ , we consider the growth of the number of irreducible factors of $V^…

math.AG2025

Quantum Elliptic Curves I: Algebraic Case

Michael J. Larsen, Valery Lunts

A complex elliptic curve $E$ can be defined as the quotient of the analytic space $C^{*}$ by a discrete action of the cyclic group $q^{Z}$ for $∣ q ∣ \neq = 1$ …

math.GR2025

Genus zero tensor products

Michael Larsen, Yue Shi

Let $L$ and $M$ be finite extensions of $K = C (t)$ . If $L \otimes_{K} M$ is a field of genus $0$ , then at least one of $L$ and $M$ is ramified over at most four valuations o…

math.PR2024

Can one hear the shape of a random walk?

Michael J. Larsen

To what extent is the underlying distribution of a finitely supported unbiased random walk on $Z$ determined by the sequence of times at which the walk returns to the orig…

math.RT2024

Sharp character bounds for symmetric groups in terms of partition length

Michael Larsen

Let $S_{n}$ denote a symmetric group, $χ$ an irreducible character of $S_{n}$ , and $g \in S_{n}$ an element which decomposes into $k$ disjoint cycles, where $1$ -cycles are included. Then…

math.GR2024

Representation growth of Fuchsian groups and modular forms

Michael Larsen, Jay Taylor, Pham Huu Tiep

Let $Γ$ be a cocompact, oriented Fuchsian group which is not on an explicit finite list of possible exceptions and $q$ a sufficiently large prime power not divisible by the order o…

math.RT2024

Bounds for $SL_{2}$ -indecomposables in tensor powers of the natural representation in characteristic $2$

Michael J. Larsen

Let $K$ be an algebraically closed field of characteristic $2$ , $G$ be the algebraic group $SL_{2}$ over $K$ , and $V$ be the natural representation of $G$ . Let $b_{k}^{G, V}$ d…

math.NT2024

On tamely ramified infinite Galois extensions

Farshid Hajir, Michael Larsen, Christian Maire +1

For a number field $K$ , we consider $K^{ta}$ the maximal tamely ramified algebraic extension of~ $K$ , and its Galois group $G_{K}^{ta} = G a l (K^{t a} / K)$ . Choose a prime $p$ such…

Robust additive bases without minimal subbases

Tensor Power Asymptotics for Linearly Reductive Groups

Quantum Elliptic Curves I: Algebraic Case

Genus zero tensor products

Can one hear the shape of a random walk?

Sharp character bounds for symmetric groups in terms of partition length

Representation growth of Fuchsian groups and modular forms

Bounds for SL2​-indecomposables in tensor powers of the natural representation in characteristic 2

On tamely ramified infinite Galois extensions

Bounds for $SL_{2}$ -indecomposables in tensor powers of the natural representation in characteristic $2$