9 papers
Diophantine rank stability and non-vanishing of -functions
Marius Fischer, Asbjørn Christian Nordentoft
Let be a modular abelian variety of analytic rank . If is a non-trivial finite abelian group such that all prime factors of are sufficiently…
Central values of additive twists of Maaà forms -functions
Sary Drappeau, Asbjørn Christian Nordentoft
In the present paper we study the central values of additive twists of Maaà forms -series. In the case of the modular group, we show that the additive twists (when averaged ove…
Horizontal -adic -functions
Daniel Kriz, Asbjørn Christian Nordentoft
We define new objects called 'horizontal -adic -functions' associated to -values of twists of elliptic curves over by characters of -power order and conduc…
Joint equidistribution of newforms
Asbjørn Christian Nordentoft, Radu Toma
Let be a compact arithmetic hyperbolic surface associated to a maximal quaternion order, let be a cover associated to an Eichler suborder of prime level , and let $Î…
Sparse Equidistribution of Geometric Invariants of Real Quadratic Fields
Peter Humphries, Asbjørn Christian Nordentoft
Duke, Imamoglu, and Tóth have recently constructed a new geometric invariant, a hyperbolic orbifold, associated to each narrow ideal class of a real quadratic field. Furthermore,…
Non-vanishing of geodesic periods of automorphic forms
Petru Constantinescu, Asbjørn Christian Nordentoft
We prove that one hundred percent of the closed geodesic periods of a Hecke--Maaà cusp form for the modular group are non-vanishing when ordered by length. We present applications…