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Publication - Ms Adelina Manzateanu

    Modular invariants for genus 3 hyperelliptic curves

    Citation

    Ionica, S, Kılıçer, P, Lauter, K, García, EL, Mânzăţeanu, A, Massierer, M & Vincent, C, 2019, ‘Modular invariants for genus 3 hyperelliptic curves’. Research in Number Theory, vol 5.

    Abstract

    In this article we prove an analogue of a theorem of Lachaud, Ritzenthaler, and Zykin, which allows us to connect invariants of binary octics to Siegel modular forms of genus 3. We use this connection to show that certain modular functions, when restricted to the hyperelliptic locus, assume values whose denominators are products of powers of primes of bad reduction for the associated hyperelliptic curves. We illustrate our theorem with explicit computations. This work is motivated by the study of the values of these modular functions at CM points of the Siegel upper half-space, which, if their denominators are known, can be used to effectively compute models of (hyperelliptic, in our case) curves with CM.

    Full details in the University publications repository