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Equidistribution Of Cusp Forms In The Level Aspect

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The unipotent mixing conjecture

Philippe Michel

We show that shifted pairs of discrete or continuous low-lying horocycles equidistribute in the product space of two modular curves. ...

Jerusalem2023

Let f(z)=q+∑n≥2a(n)qn be a weight k normalized newform with integer coefficients and trivial residual mod 2 Galois representation. We extend the results of Amir and Hong in Amir and Hong (On L-functions of modular elliptic curves and certain K3 surfaces, R ...

2021

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

SU(4) topological resonating valence bond spin liquid on the square lattice

Olivier Clément Romain Gauthé

We generalize the construction of the spin-1/2 SU(2) resonating valence bond (RVB) state to the case of the self-conjugate 6 representation of SU(4). As for the case of SU(2) [J.-Y. Chen and D. Poilblanc, Phys. Rev. B 97, 161107(R) (2018)], we use the proj ...

2019

BUSINESS TRAVELLER . How pod planes could change travel forever

Futuristic and disruptive There are several independent initiatives exploring the feasibility of modular planes, which could transform the way people and cargo travel. One of these revolutionary aircraft designs, called Clip-Air, has been created by Switze ...

2018

Status of CEA Magnet Design Tools and Applications to EU DEMO PF and CS Magnets

Kamil Sedlák

In the framework of the design activities conducted in the EU for dimensioning the future fusion demonstration reactor (DEMO), extensive analyses were carried out within the framework of the EUROfusion consortium, with the objective of defining the design ...

2018

We construct "generalized Heegner cycles" on a variety fibered over a Shimura curve, defined over a number field. We show that their images under the p-adic Abel-Jacobi map coincide with the values (outside the range of interpolation) of a p-adic L-functio ...

Oxford University Press2015

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

A review. Colloidal nanocrystal frameworks (CNFs) are a modular class of mesostructured porous materials, which are assembled from pre-formed nanocrystal building units using suitably designed block copolymer architecture-directing agents. The functional a ...

2015

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