Concept

Conjecture de Ramanujan

Publications associées (8)

Rankin-Selberg coefficients in large arithmetic progressions

Let (?(f) (n))(n=1) be the Hecke eigenvalues of either a holomorphic Hecke eigencuspform or a Hecke-Maass cusp form f. We prove that, for any fixed ? > 0, under the Ramanujan-Petersson conjecture for GL(2) Maass forms, the Rankin-Selberg coefficients (?(f) ...

SCIENCE PRESS2023

From Wallis to Ramanujan, in companionship with RW Gosper

Manuel Ojanguren

Accelerating the convergence of some hypergeometric series with Gosper's method leads, in a most elementary way, to some series discovered by Ramanujan, Bauer and Dougall. In particular, it is shown that one of them can be traced back to the well-known for ...

2018

A twisted Motohashi formula and Weyl-subconvexity for -functions of weight two cusp forms

Ian Nicholas Petrow

We derive a Motohashi-type formula for the cubic moment of central values of -functions of level cusp forms twisted by quadratic characters of conductor , previously studied by Conrey and Iwaniec and Young. Corollaries of this formula include Weyl-subconve ...

Springer Verlag2015

CM values of higher Green's functions and regularized Petersson products

Maryna Viazovska

Higher Green functions are real-valued functions of two variables on the upper half-plane, which are bi-invariant under the action of a congruence subgroup, have a logarithmic singularity along the diagonal, and satisfy the equation f = k(1−k) f ; here i ...

Cambridge UP2015

The geometry of the universal Teichmuller space and the Euler-Weil-Petersson equation

Tudor Ratiu, François Gay-Balmaz

On the identity component of the universal Teichmuller space endowed with the Takhtajan-Teo topology, the geodesics of the Weil Petersson metric are shown to exist for all time. This component is naturally a subgroup of the quasisymmetric homeomorphisms of ...

Elsevier2015

Modular Functions and Special Cycles

Maryna Viazovska

In this thesis we study algebraic cycles on Shimura varieties of orthogonal type. Such varieties are a higher dimensional generalization of modular curves and their important feature is that they have natural families of algebraic cycles in all codimesions ...

Rheinische Friedrich-Wilhelms-Universität Bonn2013

Theta lifts and local Maass forms

Maryna Viazovska

The first two authors and Kohnen have recently introduced a new class of modular objects called locally harmonic Maass forms, which are annihilated almost everywhere by the hyperbolic Laplacian operator. In this paper, we realize these locally harmonic Maa ...

2013

Expanding graphs, Ramanujan graphs, and 1-factor perturbations

Antoine Musitelli

We construct (k±1)-regular graphs which provide sequences of expanders by adding or substracting appropriate 1- factors from given sequences of k- regular graphs. We compute numerical examples in a few cases for which the given sequences are from the work ...

2006

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