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of 1 351
pro vyhledávání: '"11r29"'
Autor:
Landesman, Aaron, Levy, Ishan
We compute the average number of surjections from class groups of quadratic function fields over $\mathbb F_q(t)$ onto finite odd order groups $H$, once $q$ is sufficiently large. These yield the first known moments of these class groups, as predicte
Externí odkaz:
http://arxiv.org/abs/2410.22210
Autor:
Kadets, Borys, Keliher, Daniel
We prove a lower bound for the exponent of the relative class group $\mathrm{Pic}^0 X_1/\phi^* \mathrm{Pic}^0 X_2$ for a covering of curves $X_1 \to X_2$ over a finite field $\mathbb{F}_q$. The results improve on the existing best bounds (due to Stic
Externí odkaz:
http://arxiv.org/abs/2410.11962
Number fields and their rings of integers, which generalize the rational numbers and the integers, are foundational objects in number theory. There are several computer algebra systems and databases concerned with the computational aspects of these.
Externí odkaz:
http://arxiv.org/abs/2409.18030
Autor:
Chatterjee, Tapas, Kumar, Karishan
Let $\theta$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $\theta$ over the rationals. Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we chara
Externí odkaz:
http://arxiv.org/abs/2408.14524
Autor:
Chatterjee, Tapas, Kumar, Karishan
Let $f(x)=x^{n}+ax^{3}+bx+c$ be the minimal polynomial of an algebraic integer $\theta$ over the rationals with certain conditions on $a,~b,~c,$ and $n.$ Let $K=\mathbb{Q}(\theta)$ be a number field and $\mathcal{O}_{K}$ be the ring of integers of $K
Externí odkaz:
http://arxiv.org/abs/2408.14117
Autor:
Maarefparvar, Abbas
We prove two conjectures proposed by Chabert and Halberstadt concerning P\'olya groups of $S_4$-fields and $D_4$-fields. More generally, the latter will be proved for $D_n$-fields with $n \geq 4$ an even integer. Further, generalizing a result of Zan
Externí odkaz:
http://arxiv.org/abs/2408.09019
Let $p$ be an odd prime, let $N$ be a prime with $N \equiv 1 \pmod{p}$, and let $\zeta_p$ be a primitive $p$-th root of unity. We study the $p$-rank of the class group of $\mathbb{Q}(\zeta_p, N^{1/p})$ using Galois cohomological methods and obtain an
Externí odkaz:
http://arxiv.org/abs/2408.04481
Autor:
Iskander, Jonas, Iyer, Hari R.
The Cohen-Lenstra-Martinet heuristics lead one to conjecture that the average size of the $p$-torsion in class groups of $G$-extensions of a number field is finite. In a 2021 paper, Lemke Oliver, Wang, and Wood proved this conjecture in the case of $
Externí odkaz:
http://arxiv.org/abs/2407.19554
Autor:
Chan, Stephanie
We demonstrate that almost all elliptic curves over $\mathbb{Q}$ with prescribed torsion subgroup, when ordered by naive height, have Szpiro ratio arbitrarily close to the expected value. We also provide upper and lower bounds for the Szpiro ratio th
Externí odkaz:
http://arxiv.org/abs/2407.13850
The Euler--Kronecker constant of a number field $K$ is the ratio of the constant and the residue of the Laurent series of the Dedekind zeta function $\zeta_K(s)$ at $s=1$. We study the distribution of the Euler--Kronecker constant $\gamma_q^+$ of the
Externí odkaz:
http://arxiv.org/abs/2407.09113