Zobrazeno 1 - 10
of 419
pro vyhledávání: '"A. J. Lemke"'
Quantum cat maps are toy models in quantum chaos associated to hyperbolic symplectic matrices $A\in \operatorname{Sp}(2n,\mathbb{Z})$. The macroscopic limits of sequences of eigenfunctions of a quantum cat map are characterized by semiclassical measu
Externí odkaz:
http://arxiv.org/abs/2410.13449
Autor:
Oliver, Robert J. Lemke
Let $k$ be a number field. We provide an asymptotic formula for the number of Galois extensions of $k$ with absolute discriminant bounded by some $X \geq 1$, as $X\to\infty$. We also provide an asymptotic formula for the closely related count of exte
Externí odkaz:
http://arxiv.org/abs/2406.04033
Given a finite group G, we prove that the vector space spanned by the faithful irreducible characters of G is generated by the monomial characters in the vector space. As a consequence, we show that in any family of G-extensions of a fixed number fie
Externí odkaz:
http://arxiv.org/abs/2405.08383
Autor:
Oliver, Robert J. Lemke
A folklore conjecture asserts the existence of a constant $c_n > 0$ such that $\#\mathcal{F}_n(X) \sim c_n X$ as $X\to \infty$, where $\mathcal{F}_n(X)$ is the set of degree $n$ extensions $K/\mathbb{Q}$ with discriminant bounded by $X$. This conject
Externí odkaz:
http://arxiv.org/abs/2311.06947
We prove normal distribution laws for primes of bad semistable reduction in families of curves. As a consequence, we deduce that when ordered by height, $100\%$ of curves in these families have, in a precise sense, many such primes.
Comment: 12
Comment: 12
Externí odkaz:
http://arxiv.org/abs/2305.15874
Publikováno v:
Biogeosciences, Vol 21, Pp 1973-1984 (2024)
In the process of reworking sediments and thus shaping biogeochemical processes, marine bottom-dwelling animals are thought to play a pivotal role in many benthic environments. Bioturbation (particle reworking) includes the downward transport of part
Externí odkaz:
https://doaj.org/article/eecbb60ed9f94a7bb6467d1eee78c195
Autor:
Anderson, Theresa C., Gafni, Ayla, Hughes, Kevin, Oliver, Robert J. Lemke, Lowry-Duda, David, Thorne, Frank, Wang, Jiuya, Zhang, Ruixiang
We study the number of degree $n$ number fields with discriminant bounded by $X$. In this article, we improve an upper bound due to Schmidt on the number of such fields that was previously the best known upper bound for $6 \leq n \leq 94$.
Comme
Comme
Externí odkaz:
http://arxiv.org/abs/2204.01651
We determine the average size of the 3-torsion in class groups of $G$-extensions of a number field when $G$ is any transitive $2$-group containing a transposition, for example $D_4$. It follows from the Cohen--Lenstra--Martinet heuristics that the av
Externí odkaz:
http://arxiv.org/abs/2110.07712
Autor:
Anderson, Theresa C., Gafni, Ayla, Oliver, Robert J. Lemke, Lowry-Duda, David, Shakan, George, Zhang, Ruixiang
We study two polynomial counting questions in arithmetic statistics via a combination of Fourier analytic and arithmetic methods. First, we obtain new quantitative forms of Hilbert's Irreducibility Theorem for degree $n$ polynomials $f$ with $\mathrm
Externí odkaz:
http://arxiv.org/abs/2107.02914
Let $k$ be a number field and $G$ be a finite group. Let $\mathfrak{F}_{k}^{G}(Q)$ be the family of number fields $K$ with absolute discriminant $D_K$ at most $Q$ such that $K/k$ is normal with Galois group isomorphic to $G$. If $G$ is the symmetric
Externí odkaz:
http://arxiv.org/abs/2012.14422