5 papers
Pseudodifferential arithmetic, Riemann and Lindelöf hypotheses
André Unterberger, André Unterberger
The Weyl symbolic calculus of operators leads to the construction, if one takes for symbol a certain distribution decomposing over the zeros of the Riemann zeta function, of an ope…
A unified scheme of approach to the Ramanujan conjecture
Andre Unterberger
The Ramanujan conjecture for modular forms of holomorphic type was proved by Deligne almost half a century ago: the proof, based on his earlier proof of Weil's conjectures, was an…
The Ramanujan-Petersson and Selberg conjectures for Maass forms
Andr'e Unterberger
We prove the Ramanujan-Petersson conjecture for Maass forms of the group , with the help of automorphic distribution theory and pseudodifferential analysis. The first noti…
Automorphic line measures in the half-plane and the Grand Riemann Hypothesis
Andre Unterberger
Poincare-type series, such as Selberg's, are known to produce automorphic functions, in the hyperbolic half-plane, the decompositions of which into eigenfunctions (genuine or gener…
Pseudodifferential arithmetic and the Riemann hypothesis: reminders
André Unterberger
The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first…