H. Au-Yeung

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math.NT2026

An upper bound for valuations of elliptic nets at primes of bad reduction

Hang Lok Edison Au-Yeung

Let $E / K$ be an elliptic curve over a field defined by the short Weierstrass equation and let $P = (P_{1}, P_{2}) \in E (K)^{2} ∖ {(O, O), (\pm P, \pm P)}$ be a pair of no…

math.NT2026

Higher rank elliptic sieve via CM endomorphisms

Hang Lok Edison Au-Yeung

A theorem of Landau and Ramanujan states that almost all integers are not sums of two squares (when ordered by their absolute value). Equivalently, almost all integers are not norm…

math.NT2025

Explicit valuation of elliptic nets for elliptic curves with complex multiplication

Edison H L Au-Yeung

Division polynomials associated to an elliptic curve $E / K$ are polynomials $ϕ_{n}, ψ_{n}^{2}$ that arise from the sequence of points ${n P}_{n \in N}$ on this curve. If one wishes to s…