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Writing CFT correlation functions as AdS scattering amplitudes

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The fourth moment of individual Dirichlet L-functions on the critical line

Berke Topacogullari

We prove an asymptotic formula for the second moment of a product of two Dirichlet L-functions on the critical line, which has a power saving in the error term and which is uniform with respect to the involved Dirichlet characters. As special cases we give ...

2020

Thermal CFTs in momentum space

Andrea Manenti

We study some aspects of conformal field theories at finite temperature in momentum space. We provide a formula for the Fourier transform of a thermal conformal block and study its analytic properties. In particular we show that the Fourier transform vanis ...

SPRINGER2020

Fourier interpolation on the real line

Maryna Viazovska

In this paper we construct an explicit interpolation formula for Schwartz functions on the real line. The formula expresses the value of a function at any given point in terms of the values of the function and its Fourier transform on the set {0,+/- 1,+/- ...

2019

Simulating background shear flow in local gyrokinetic simulations

Stephan Brunner, Justin Richard Ball, Ben McMillan

Local gyrokinetic simulations solve the gyrokinetic equations with homogeneous background gradients, typically using a doubly periodic domain in the (x, y) plane (i.e. perpendicular to the field line). Spatial Fourier representations are almost universal i ...

2019

Analytic twists of modular forms and applications

Alexandre François Peyrot

We are interested in the study of non-correlation of Fourier coefficients of Maass forms against a wide class of real analytic functions. In particular, the class of functions we are interested in should be thought of as some archimedean analogs of Frobeni ...

EPFL2017

On Short Sums Of Trace Functions

Philippe Michel, Chandra Sekhar Raju

We consider sums of oscillating functions on intervals in cyclic groups of size close to the square root of the size of the group. We first prove non-trivial estimates for intervals of length slightly larger than this square root (bridging the "Polya-Vinog ...

Annales Inst Fourier2017

Factorization of Mellin amplitudes

We introduce Mellin amplitudes for correlation functions of k scalar operators and one operator with spin in conformal field theories (CFT) in general dimension. We show that Mellin amplitudes for scalar operators have simple poles with residues that facto ...

Springer2015

Asymptotic bifurcation and second order elliptic equations on R-N

Charles Stuart

This paper deals with asymptotic bifurcation, first in the abstract setting of an equation G(u) = lambda u, where G acts between real Hilbert spaces and lambda is an element of R, and then for square-integrable solutions of a second order non-linear ellipt ...

Elsevier Science Bv2015

Spinning AdS propagators

We develop the embedding formalism to describe symmetric traceless tensors in Anti-de Sitter space. We use this formalism to construct the bulk-to-bulk propagator of massive spin J fields and check that it has the expected short distance and massless limit ...

Springer2014

Regularity results for very degenerate elliptic equations

Maria Colombo

We consider a family of elliptic equations introduced in the context of traffic congestion. They have the form del . (del F(del u)) = f where F is a convex function which vanishes inside some convex set and is elliptic outside. Under some natural assumptio ...

2014