7 citations · 21 across the 18 of their papers we have counts for
19 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…
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 $ι…
-adic moments of -functions
Daniel Kriz, Asbjørn Christian Nordentoft
We obtain a formula for the -adic valuation of weighted moments of central -values of holomorphic cusp forms twisted by Dirichlet characters of order . In some cases we gi…
Equidistribution of partial coverings from closed geodesics
Asbjørn Christian Nordentoft, Ser Peow Tan
Given a finite volume hyperbolic surface, a fundamental polygon and an oriented closed geodesic, we associate a partial covering of the surface. We prove that given a sequence of c…
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--Maaß cusp form for the modular group are non-vanishing when ordered by length. We present applications…
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…
Equidistribution of -orbits of closed geodesics
Asbjørn Christian Nordentoft
Given an element of we associate a closed geodesic on the modular surface. We prove that the closed geodesics associated to cosets of sufficiently…
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, t…
Central values of additive twists of Maaß forms -functions
Sary Drappeau, Asbjørn Christian Nordentoft
In the present paper we study the central values of additive twists of Maaß forms -series. In the case of the modular group, we show that the additive twists (when averaged over…
Concentration of closed geodesics in the homology of modular curves
Asbjørn Christian Nordentoft
We prove that the homology classes of closed geodesics associated to subgroups of narrow class groups of real quadratic fields concentrate around the Eisenstein line. This fits int…
Wide moments of -functions II: Dirichlet -functions
Asbjørn Christian Nordentoft
We study wide moments of Dirichlet -functions using analytic properties of the Lerch zeta function. Among other things we obtain an asymptotic expansion of wide moments of Diric…
Wide moments of -functions I: Twists by class group characters of imaginary quadratic fields
Asbjorn Christian Nordentoft
We calculate certain "wide moments" of central values of Rankin--Selberg -functions where is a cuspidal automorphic representation of ov…
Bounds on shifted convolution sums for Hecke eigenforms
Asbjorn Christian Nordentoft, Yiannis N. Petridis, Morten S. Risager
Shifted convolution sums play a prominent rôle in analytic number theory. We investigate pointwise bounds, mean-square bounds, and average bounds for shifted convolution sums for H…
Small scale equidistribution of Hecke eigenforms at infinity
Asbjorn Christian Nordentoft, Yiannis N. Petridis, Morten S. Risager
We investigate the equidistribution of Hecke eigenforms on sets that are shrinking towards infinity. We show that at scales finer than the Planck scale they do not equidistribute w…
Residual equidistribution of modular symbols and cohomology classes for quotients of hyperbolic -space
Asbjorn Christian Nordentoft, Petru Constantinescu
We provide a new and simple automorphic method using Eisenstein series to study the equidistribution of modular symbols modulo primes, which we apply to prove an average version of…
A note on additive twists, reciprocity laws and quantum modular forms
Asbjorn Christian Nordentoft
We prove that the central values of additive twists of a cuspidal -function define a quantum modular form in the sense of Zagier, generalizing recent results of Bettin and Drapp…
On the distribution of periods of holomorphic cusp forms and zeroes of period polynomials
Asbjorn Christian Nordentoft
In this paper we determine the limiting distribution of the image of the Eichler--Shimura map or equivalently the limiting joint distribution of the coefficients of the period poly…
Hybrid subconvexity for class group -functions and uniform sup norm bounds of Eisenstein series
Asbjorn Christian Nordentoft
In this paper we prove a hybrid subconvexity bound for class group -functions associated to a quadratic extension (real or imaginary). Our proof relies on relatin…
Central values of additive twists of cuspidal -functions
Asbjorn Christian Nordentoft
Additive twists are important invariants associated to holomorphic cusp forms; they encode the Eichler--Shimura isomorphism and contain information about automorphic -functions.…