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math.NT2026
Elliptic butterflies
Jean-Marc Couveignes, Reynald Lercier
We study natural evaluation and interpolation problems for elliptic functions and prove that they allow a recursive treatment using a variant of classical butterflies first introdu…
math.NT2024
Reduction of Plane Quartics and Dixmier-Ohno invariants
Raymond van Bommel, Jordan Docking, Reynald Lercier +1
We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determini…
math.NT2024
Siegel modular forms of degree three and invariants of ternary quartics
Reynald Lercier, Christophe Ritzenthaler
We determine the structure of the graded ring of Siegel modular forms of degree 3. It is generated by 19 modular forms, among which we identify a homogeneous system of parameters w…