Computing Hilbert modular forms as orthogonal modular forms
We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.
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arXiv subjects
Gonzalo Tornaria
Publications and source records attributed to Gonzalo Tornaria.
A database of paramodular forms from quinary orthogonal modular forms
We compute tables of paramodular forms of degree two and cohomological weight via a correspondence with orthogonal modular forms on quinary lattices.
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On the paramodularity of typical abelian surfaces (and reduction of G-covariant bilinear forms)
Generalizing the method of Faltings-Serre, we rigorously verify that certain abelian surfaces without extra endomorphisms are paramodular. To compute the required Hecke eigenvalues, we develop a method of specialization of Siegel paramodular forms to modular curves. In the appendix, Serre proves a result extending his work on the reduction of G-invariant bilinear forms modulo primes to the case of G-covariant forms.
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Nonvanishing of twists of $L$-functions attached to Hilbert modular forms
We describe algorithms for computing central values of twists of $L$-functions associated to Hilbert modular forms, carry out such computations for a number of examples, and compare the results of these computations to some heuristics and predictions from random matrix theory.
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Examples of Shimura correspondence for level p^2 and real quadratic twists
We give examples of Shimura correspondence for rational modular forms f of weight 2 and level p^2, for primes p<=19, computed as an application of a method we introduced in \cite{Pacetti-Tornaria}. Furthermore, we verify in this examples a conjectural formula for the central values L(f,-pd,1) and, in case p = 3 (mod 4), a formula for the central values L(f,d,1) corresponding to the real quadratic twists of f.
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