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2 results

THEOREM OF WARD ON SYMMETRIES OF ELLIPTIC NETS
Part of
L. DEWAGHE
Journal:

Bulletin of the Australian Mathematical Society , First View

Published online by Cambridge University Press:

04 October 2024, pp. 1-14
- Article
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We present a new version of a generalisation to elliptic nets of a theorem of Ward [‘Memoir on elliptic divisibility sequences’, Amer. J. Math. 70 (1948), 31–74] on symmetry of elliptic divisibility sequences. Our results cover all that is known today.

Common valuations of division polynomials
Part of
- Arithmetic algebraic geometry
- Curves
Bartosz Naskręcki, Matteo Verzobio
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View

Published online by Cambridge University Press:

26 February 2024, pp. 1-15
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In this note, we prove a formula for the cancellation exponent $k_{v,n}$ between division polynomials $\psi _n$ and $\phi _n$ associated with a sequence $\{nP\}_{n\in \mathbb {N}}$ of points on an elliptic curve $E$ defined over a discrete valuation field $K$. The formula greatly generalizes the previously known special cases and treats also the case of non-standard Kodaira types for non-perfect residue fields.