Zobrazeno 1 - 10
of 51
pro vyhledávání: '"Scheidler, Renate"'
We present two new algorithms for solving norm equations over global function fields with at least one infinite place of degree 1 and no wild ramification. The first of these is a substantial improvement of a method due to Ga\'{a}l and Pohst, while t
Externí odkaz:
http://arxiv.org/abs/2401.16644
Autor:
Arpin, Sarah, Chen, Mingjie, Lauter, Kristin E., Scheidler, Renate, Stange, Katherine E., Tran, Ha T. N.
The paper concerns several theoretical aspects of oriented supersingular $\ell$-isogeny volcanoes and their relationship to closed walks in the supersingular $\ell$-isogeny graph. Our main result is a bijection between the rims of the union of all or
Externí odkaz:
http://arxiv.org/abs/2205.03976
Autor:
Arpin, Sarah, Chen, Mingjie, Lauter, Kristin E., Scheidler, Renate, Stange, Katherine E., Tran, Ha T. N.
In supersingular isogeny-based cryptography, the path-finding problem reduces to the endomorphism ring problem. Can path-finding be reduced to knowing just one endomorphism? It is known that a small endomorphism enables polynomial-time path-finding a
Externí odkaz:
http://arxiv.org/abs/2201.11079
An $(a,b)$-difference necklace of length $n$ is a circular arrangement of the integers $0, 1, 2, \ldots , n-1$ such that any two neighbours have absolute difference $a$ or $b$. We prove that, subject to certain conditions on $a$ and $b$, such arrange
Externí odkaz:
http://arxiv.org/abs/2006.15250
We present computational results on the divisor class number and the regulator of a cubic function field over a large base field. The underlying method is based on approximations of the Euler product representation of the zeta function of such a fiel
Externí odkaz:
http://arxiv.org/abs/1601.03309
Autor:
Bouw, Irene, Ho, Wei, Malmskog, Beth, Scheidler, Renate, Srinivasan, Padmavathi, Vincent, Christelle
This paper describes a class of Artin-Schreier curves, generalizing results of Van der Geer and Van der Vlugt to odd characteristic. The automorphism group of these curves contains a large extraspecial group as a subgroup. Precise knowledge of this s
Externí odkaz:
http://arxiv.org/abs/1410.7031
We present a method for tabulating all cubic function fields over $\mathbb{F}_q(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb{F}_{q}^*$, up to a given bound $B$ on the
Externí odkaz:
http://arxiv.org/abs/1004.4785
This paper presents an algorithm for generating all imaginary and unusual discriminants up to a fixed degree bound that define a quadratic function field of positive 3-rank. Our method makes use of function field adaptations of a method due to Belaba
Externí odkaz:
http://arxiv.org/abs/1003.1287
We describe and give computational results of a procedure to compute the divisor class number and regulator of most purely cubic function fields of unit rank 2. Our implementation is an improvement to Pollard's Kangaroo method in infrastructures, usi
Externí odkaz:
http://arxiv.org/abs/1001.4095