Adrien Poteaux, Martin Weimann
Published 2024-05-22Version 1
We obtain new complexity bounds for computing a triangular integral basis of a number field or a function field. We reach for function fields a softly linear cost with respect to the size of the output when the residual characteristic is zero or big enough. Analogous results are obtained for integral basis of fractional ideals, key ingredients towards fast computation of Riemann-Roch spaces. The proof is based on the recent fast OM algorithm of the authors and on the MaxMin algorithm of Stainsby, together with optimal truncation bounds and a precise complexity analysis.
Genus growth in $\mathbb{Z}_p$-towers of function fields
The Manin constant of elliptic curves over function fields
On the distribution of the of Frobenius elements on elliptic curves over function fields
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