Zobrazeno 1 - 10
of 378
pro vyhledávání: '"11m38"'
Autor:
Booher, Jeremy, Pries, Rachel
For every prime number $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. This extends earlier work of Ekedahl and of Harashita, Kudo, and Senda.
Externí odkaz:
http://arxiv.org/abs/2410.20262
Autor:
Gao, Peng, Zhao, Liangyi
We establish sharp upper bounds on shifted moments of quadratic Dirichlet $L$-functions over function fields. As an application, we prove some bounds for moments of quadratic Dirichlet character sums over function fields.
Comment: 10 pages
Comment: 10 pages
Externí odkaz:
http://arxiv.org/abs/2408.02880
In \cite{FGHP}, the first author and his collaborators proved an equivariant Tamagawa number formula for the special value at $s=0$ of a Goss--type $L$--function, equivariant with respect to a Galois group $G$, and associated to a Drinfeld module def
Externí odkaz:
http://arxiv.org/abs/2406.13976
Autor:
Gezmiş, Oğuz, Green, Nathan
We introduce formulas for the logarithms of Drinfeld modules using a framework recently developed by the second author. We write the logarithm function as the evaluation under a motivic map of a product of rigid analytic trivializations of $t$-motive
Externí odkaz:
http://arxiv.org/abs/2405.02915
Zagier-Hoffman's conjectures predict the dimension and a basis for the $\mathbb Q$-vector spaces spanned by $N$th cyclotomic multiple zeta values (MZV's) of fixed weight where $N$ is a natural number. For $N=1$ (MZV's case), half of these conjectures
Externí odkaz:
http://arxiv.org/abs/2402.11539
Let $C$ and $C'$ be curves over a finite field $K$, provided with embeddings $\iota$ and $\iota'$ into their Jacobian varieties. Let $D\to C$ and $D'\to C'$ be the pullbacks (via these embeddings) of the multiplication-by-$2$ maps on the Jacobians. W
Externí odkaz:
http://arxiv.org/abs/2402.08853
Autor:
Kramer-Miller, Joe, Upton, James
Let $X$ be a smooth proper curve over a finite field and let $\infty \in X$ be a closed point. Let $A$ be the ring of functions on $X - \infty$. The Goss zeta function $\zeta_A$ of $A$ is an equicharacteristic analogue of the Riemann zeta function. I
Externí odkaz:
http://arxiv.org/abs/2312.01264
For a fixed positive integer $e$, we describe an algorithm for computing, for all primes $p \leq X$, the mod-$p^e$ reduction of the trace of Frobenius at $p$ of a fixed hypergeometric motive over $\mathbb{Q}$ in time quasilinear in $X$. This extends
Externí odkaz:
http://arxiv.org/abs/2310.06971
Let $X$ be a smooth irreducible projective curve of genus $g \geq 2$ over a finite field $\F_{q}$ of characteristic $p$ with $q$ elements such that the function field $\F_{q}(X)$ is a geometric Galois extension of the rational function field of degre
Externí odkaz:
http://arxiv.org/abs/2309.15085
Autor:
Pries, Rachel
This paper contains a method to prove the existence of smooth curves in positive characteristic whose Jacobians have unusual Newton polygon. Using this method, I give a new proof that there exist supersingular curves of genus $4$ for every prime $p$.
Externí odkaz:
http://arxiv.org/abs/2306.11080