Zobrazeno 1 - 10
of 23 569
pro vyhledávání: '"function field"'
Autor:
Sawin, Will
We propose a refinement of the random matrix model for a certain family of $L$-functions over $\mathbb F_q[u]$, using techniques that we hope will eventually apply to an arbitrary family of $L$-functions. This consists of a probability distribution o
Externí odkaz:
http://arxiv.org/abs/2409.02876
Autor:
Ghosh, Sohan, Ray, Jishnu
Consider a function field $K$ with characteristic $p>0$. We investigate the $\Lambda$-module structure of the Mordell-Weil group of an abelian variety over $\mathbb{Z}_p$-extensions of $K$, generalizing results due to Lee. Next, we study the algebrai
Externí odkaz:
http://arxiv.org/abs/2406.03201
Autor:
Wessel, Mieke
We prove some new instances of a conjecture of Bachoc, Couvreur and Z\'emor that generalizes Freiman's $3k-4$ Theorem to a multiplicative version in a function field setting. As a consequence we find that if $F$ is a rational function field over an a
Externí odkaz:
http://arxiv.org/abs/2405.10724
In this article we continue the work started in arXiv:2303.00376v1, explicitly determining the Weierstrass semigroup at any place and the full automorphism group of a known $\mathbb{F}_{q^2}$-maximal function field $Y_3$ having the third largest genu
Externí odkaz:
http://arxiv.org/abs/2404.18808
Autor:
Entin, Alexei
For a fixed prime power $q$ and natural number $d$ we consider a random polynomial $$f=x^n+a_{n-1}(t)x^{n-1}+\ldots+a_1(t)x+a_0(t)\in\mathbb F_q[t][x]$$ with $a_i$ drawn uniformly and independently at random from the set of all polynomials in $\mathb
Externí odkaz:
http://arxiv.org/abs/2403.11943
Let $F=F|\mathbb{K}$ a be function field over an algebraically closed constant field $\mathbb{K}$ of positive characteristic $p$. For a $\mathbb{K}$-automorphism group $G$ of $F$, the invariant of $G$ is the fixed field $F^G$ of $G$. If $F$ has trans
Externí odkaz:
http://arxiv.org/abs/2312.13751
We use a function field version of the circle method to prove that a positive proportion of elements in $\mathbb{F}_q[t]$ are representable as a sum of three cubes of minimal degree from $\mathbb{F}_q[t]$, assuming a suitable form of the Ratios Conje
Externí odkaz:
http://arxiv.org/abs/2402.07146
Autor:
Dinesh S Thakur
This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations),
Akademický článek
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