Concept
Selberg trace formula
Related publications (14)
Algebraic twists of GL(2) automorphic forms
In this thesis we consider the problem of estimating the correlation of Hecke eigenvalues of GL2 automorphic forms with a class of functions of algebraic origin defined over finite fields called trace functions. The class of trace functions is vast and inc ...
EPFL2023Power variations in fractional Sobolev spaces for a class of parabolic stochastic PDEs
Robert Dalang, Carsten Hao Ye Chong
We consider a class of parabolic stochastic PDEs on bounded domains D c Rd that includes the stochastic heat equation but with a fractional power gamma of the Laplacian. Viewing the solution as a process with values in a scale of fractional Sobolev spaces ...
INT STATISTICAL INST2023On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem
We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...
MATHEMATICAL SCIENCE PUBL2021Adaptive Social Learning
Ali H. Sayed, Virginia Bordignon
This work proposes a novel strategy for social learning by introducing the critical feature of adaptation. In social learning, several distributed agents update continually their belief about a phenomenon of interest through: i) direct observation of strea ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021MULTIPLICITY AND CONCENTRATION RESULTS FOR SOME NONLINEAR SCHRODINGER EQUATIONS WITH THE FRACTIONAL p-LAPLACIAN
We consider a class of parametric Schrodinger equations driven by the fractional p-Laplacian operator and involving continuous positive potentials and nonlinearities with subcritical or critical growth. Using variational methods and Ljusternik-Schnirelmann ...
2018Algebraic twists of modular forms and Hecke orbits
We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistri ...
Springer Verlag2015Algebraic Trace Functions Over The Primes
We study sums over primes of trace functions of l-adic sheaves. Using an extension of our earlier results on algebraic twists of modular forms to the case of Eisenstein series and bounds for Type II sums based on similar applications of the Riemann hypothe ...
Duke Univ Press2014Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields
We prove upper bounds for Hecke-Laplace eigenfunctions on certain Riemannian manifolds X of arithmetic type, uniformly in the eigenvalue and the volume of the manifold. The manifolds under consideration are d-fold products of 2-spheres or 3-spheres, realiz ...
Cambridge Univ Press2013