Zobrazeno 1 - 10
of 580
pro vyhledávání: '"11r58"'
Autor:
Nguyen, Tung T., Tân, Nguyen Duy
A graph is called integral if its eigenvalues are integers. In this article, we provide the necessary and sufficient conditions for a Cayley graph over a finite symmetric algebra $R$ to be integral. This generalizes the work of So who studies the cas
Externí odkaz:
http://arxiv.org/abs/2411.00307
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
We obtain explicit upper and lower bounds on the size of the coefficients of the Drinfeld modular polynomials $\Phi_N$ for any monic $N\in\mathbb{F}_q[t]$. These polynomials vanish at pairs of $j$-invariants of Drinfeld $\mathbb{F}_q[t]$-modules of r
Externí odkaz:
http://arxiv.org/abs/2410.11132
Autor:
N, Darsana, Rout, S. S.
Let $(U_n)_{n\geq 0}$ be a non-degenerate linear recurrence sequence with order at least two defined over a function field and $\mathcal{O}_S^*$ be the set of $S$-units. In this paper, we use a result of Brownawell and Masser to prove effective resul
Externí odkaz:
http://arxiv.org/abs/2408.09448
We prove that the dual fine Selmer group of an abelian variety over the unramified $\mathbb{Z}_{p}$-extension of a function field is finitely generated over $\mathbb{Z}_{p}$. This is a function field version of a conjecture of Coates--Sujatha. We fur
Externí odkaz:
http://arxiv.org/abs/2408.06938
We give several formulas for how Iwasawa $\mu$-invariants of abelian varieties over unramified $\mathbb{Z}_{p}$-extensions of function fields change under isogeny. These are analogues of Schneider's formula in the number field setting. We also prove
Externí odkaz:
http://arxiv.org/abs/2407.21431
Let $v$ be a finite place of $\mathbb{F}_q(\theta)$. We show that algebraic relations of $v$-adic arithmetic gamma values over $\mathbb{F}_q(\theta)$ are explained by the standard functional equations together with Thakur's analogue of the Gross-Kobl
Externí odkaz:
http://arxiv.org/abs/2407.15024
We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the structure o
Externí odkaz:
http://arxiv.org/abs/2407.10783
We consider the generalization of the extended genus field of a prime degree cyclic Kummer extension of a rational function field obtained by R. Clement in 1992 to general Kummer extensions. We observe that the same approach of Clement works in gener
Externí odkaz:
http://arxiv.org/abs/2403.01021