7 papers
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, Riemann and Lindelöf hypotheses
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…
Pseudodifferential arithmetic and a failed attempt on the Riemann hypothesis
Andre Unterberger
A criterion for the validity of the Riemann hypothesis reduced the problem to the search for a certain estimate, for a hermitian form associated by means of the Weyl symbolic calcu…
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…
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…