15 citations · 37 across the 6 of their papers we have counts for
6 papers
An explicit inversion formula for the -adic Whittaker transform on
João Guerreiro
Whittaker functions on non-archimedean fields were first introduced in the work of Jacquet, and they were characterized explicitly by Shintani. We obtain an explicit inversion form…
Mean square in the prime geodesic theorem
Giacomo Cherubini, João Guerreiro
We prove upper bounds for the mean square of the remainder in the prime geodesic theorem, for every cofinite Fuchsian group, which improve on average on the best known pointwise bo…
Traces, high powers and one level density for families of curves over finite fields
Alina Bucur, Edgar Costa, Chantal David +2
The zeta function of a curve over a finite field may be expressed in terms of the characteristic polynomial of a unitary matrix . We develop and present a new technique to…
Monochromatic paths for the integers
João Guerreiro, Imre Z. Ruzsa, Manuel Silva
Recall that van der Waerden's theorem states that any finite coloring of the naturals has arbitrarily long monochromatic arithmetic sequences. We explore questions about the set of…
An orthogonality relation for a thin family of Maass forms
João Guerreiro
We prove an orthogonality relation for the Fourier-Whittaker coefficients of a thin family of Maass forms containing all self-dual forms. This is obtained by analysing the…
Asymptotic expansions, -values and a new Quantum Modular Form
Edgar Costa, Korneel Debaene, João Guerreiro
In 2010 Zagier introduced the notion of a quantum modular form. One of his first examples was the "strange" function of Kontsevich. Here we produce a new example of a quantu…