Peter Vang Uttenthal

activity

20232026

most citedA classification of even representations onto 3-adic SL(2)

1 citations · 1 across the 11 of their papers we have counts for

collaborators

12 papers

math.NT2026

Fine structure of even Galois deformation rings

Peter Vang Uttenthal

For every even Galois representation in a family of prime conductor $ℓ$ , we prove that if $k \in Z_{\geq 1}$ is maximal such that \[\ell \equiv 1 \bmod 3^k\] then the e…

math.RT2026

Positive kernels in Lie group representations and Fourier interpolation

Peter Vang Uttenthal

For a given function $f$ on a discrete subspace $Γ$ of a noncompact Riemannian symmetric space $G / K$ , we construct analytic, noncompactly supported functions $W$ on $G / K$ with $W|_…

math.FA2026

Convergent series of coherent states

Peter Vang Uttenthal

For a discrete subspace $Γ$ of a homogeneous space $X$ and a positive definite reproducing kernel Hilbert space $H (X)$ , a convergence proof is given for series of partial…

math.RT2026

Covers of Bruhat-Tits trees

Corina Ciobotaru, Peter Vang Uttenthal

Let $G$ be a locally compact group and let $G$ be a central extension that splits over a maximal compact subgroup $K$ of $G$ . We derive an explicit cocycle that lifts t…

math.NT2025★ 1 cited

A classification of even representations onto 3-adic SL(2)

Peter Vang Uttenthal

This paper gives a classification of even representations onto $SL (2, Z_{3})$ of prime conductor. In addition, an explicit algorithm based on global class fiel…

math.NT2025

Parameters of solvable automorphic forms

Peter Vang Uttenthal

In a letter from Tate to Serre dated March 26, 1974, Tate suggested a classification of weight one modular forms of prime level in terms of their associated odd Artin representatio…

math.NT2025

The spin of prime ideals and level-raising of even Galois representations

Marius Fischer, Peter Vang Uttenthal

By extending the notion of spin of prime ideals, we show that a short character sum conjecture implies that the set of primes raising the level of a certain even Galois representat…

math.NT2024

Elliptic curves and spin

Peter Koymans, Peter Vang Uttenthal

In the early 2000s, Ramakrishna asked the question: For the elliptic curve $E : y^{2} = x^{3} - x,$ what is the density of primes $p$ for which the Fourier coefficient $a_{p} (E)$ is a…

math.RT2024

Whitney extensions on symmetric spaces

Birgit Speh, Peter Vang Uttenthal

In 1934, H. Whitney introduced the problem of extending a function on a set of points in $R^{n}$ to an analytic function on the ambient space. In this article we prove Whitn…

math.NT2023

Level-raising of even representations of tetrahedral type and equidistribution of lines in the projective plane

Peter Vang Uttenthal

The distribution of primes raising the level of even Galois representations of tetrahedral type is studied. Data are presented on primes $v \leq 1 0^{8}$ raising the level of $3$ -adic…

math.NT2023

On flat even deformation rings

Peter Vang Uttenthal

In the presence of a nontrivial dual Selmer group, certain global even deformation rings are shown to be finite and flat over $Z_{p}$ . Previously, flatness was only known in…

math.NT2023

Density of Selmer ranks in families of even Galois representations, Wiles' formula, and global reciprocity

Peter Vang Uttenthal

This paper concerns the distribution of Selmer ranks in a family of even Galois representations in even residual characteristic obtained by allowing ramification at auxiliary prime…