Zobrazeno 1 - 10
of 54
pro vyhledávání: '"Tornaría, Gonzalo"'
We compute tables of paramodular forms of degree two and cohomological weight via a correspondence with orthogonal modular forms on quinary lattices.
Comment: 17 pages, to appear in the LuCaNT proceedings
Comment: 17 pages, to appear in the LuCaNT proceedings
Externí odkaz:
http://arxiv.org/abs/2308.09824
Let $\mathcal{C}$ be a hyperelliptic curve $y^2 = p(x)$ defined over a number field $K$ with $p(x)$ integral of odd degree. The purpose of the present article is to prove lower and upper bounds for the $2$-Selmer group of the Jacobian of $\mathcal{C}
Externí odkaz:
http://arxiv.org/abs/2308.08663
We work out the exact relationship between algebraic modular forms for a two-by-two general unitary group over a definite quaternion algebra, and those arising from genera of positive-definite quinary lattices, relating stabilisers of local lattices
Externí odkaz:
http://arxiv.org/abs/2112.03797
Autor:
Sirolli, Nicolás, Tornaría, Gonzalo
Given a Hilbert cuspidal newform $g$ we construct a family of modular forms of half-integral weight whose Fourier coefficients give the central values of the twisted $L$-series of $g$ by fundamental discriminants. The family is parametrized by quadra
Externí odkaz:
http://arxiv.org/abs/2107.04483
Let $K$ be a number field and $E/K$ be an elliptic curve with no $2$-torsion points. In the present article we give lower and upper bounds for the $2$-Selmer rank of $E$ in terms of the $2$-torsion of a narrow class group of a certain cubic extension
Externí odkaz:
http://arxiv.org/abs/2001.02263
Autor:
Sirolli, Nicolás, Tornaría, Gonzalo
We describe a construction of preimages for the Shimura map on Hilbert modular forms using generalized theta series, and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted $L$-functions. This fo
Externí odkaz:
http://arxiv.org/abs/1812.11635
Publikováno v:
Alg. Number Th. 13 (2019) 1145-1195
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
Externí odkaz:
http://arxiv.org/abs/1805.10873
Autor:
Sirolli, Nicolás, Tornaría, Gonzalo
Publikováno v:
Trans. Amer. Math. Soc. 370 (2018), 6153-6168
We describe a construction of preimages for the Shimura map on Hilbert modular forms, and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted L-functions. Our construction is inspired by that of
Externí odkaz:
http://arxiv.org/abs/1603.03753
Publikováno v:
LMS J. Comput. Math. 19 (2016) 205-219
We describe an implementation for computing holomorphic and skew-holomorphic Jacobi forms of integral weight and scalar index on the full modular group. This implementation is based on formulas derived by one of the authors which express Jacobi forms
Externí odkaz:
http://arxiv.org/abs/1602.07021
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
Externí odkaz:
http://arxiv.org/abs/1405.6059