Publications associées à Algebraic twists of modular forms and Hecke orbits

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Arithmetic and geometric structures in cryptography

Benjamin Pierre Charles Wesolowski

We explore a few algebraic and geometric structures, through certain questions posed by modern cryptography. We focus on the cases of discrete logarithms in finite fields of small characteristic, the structure of isogeny graphs of ordinary abelian varietie ...

EPFL2018

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Elisabetta Chiodaroli

We study the Riemann problem for multidimensional compressible isentropic Euler equations. Using the framework developed in Chiodaroli et al (2015 Commun. Pure Appl. Math. 68 1157-90), and based on the techniques of De Lellis and Szekelyhidi (2010 Arch. Ra ...

IOP PUBLISHING LTD2018

Some applications of smooth bilinear forms with Kloosterman sums

Philippe Michel

We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier resul ...

Maik Nauka/Interperiodica/Springer2017

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Amer Mathematical Soc2017

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

The Particle-In-Fourier (PIF) Approach Applied to Gyrokinetic Simulations

Laurent Villard, Stephan Brunner, Emmanuel Lanti, Noé Thomas Elie Ohana, Claudio Gheller, Aaron Lewis Scheinberg

A widespread method for gyrokinetic simulations relies on the discretization of distribution functions with numerical markers. The electromagnetic field is typically represented on a grid by finite differences or finite elements (Particle-In-Cell, PIC). Wh ...

2017

Large Sieve Inequalities for Algebraic Trace Functions

Philippe Michel, Ping Xi

The large sieve inequalities for algebraic trace functions are considered in this article. A fundamental iterative relation is established by classical Fourier analysis, and l-adic Fourier analysis and multiplicative convolutions of sheaves are also requir ...

Oxford Univ Press2017

On Moments Of Twisted L-Functions

Philippe Michel

We study the average of the product of the central values of two L-functions of modular forms f and g twisted by Dirichlet characters to a large prime modulus q. As our principal tools, we use spectral theory to develop bounds on averages of shifted convol ...

Johns Hopkins Univ Press2017

Algebraic twists of modular forms and Hecke orbits

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Arithmetic and geometric structures in cryptography

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Bilinear forms with Kloosterman sums and applications

Analytic twists of modular forms and applications

Some applications of smooth bilinear forms with Kloosterman sums

Patching And Weak Approximation In Isometry Groups

On Short Sums Of Trace Functions

The Particle-In-Fourier (PIF) Approach Applied to Gyrokinetic Simulations

Large Sieve Inequalities for Algebraic Trace Functions

On Moments Of Twisted L-Functions

Large Sieve Inequalities for Algebraic Trace Functions

Patching And Weak Approximation In Isometry Groups

Some applications of smooth bilinear forms with Kloosterman sums

Bilinear forms with Kloosterman sums and applications

On Moments Of Twisted L-Functions

Non-uniqueness of admissible weak solutions to the Riemann problem for isentropic Euler equations

Arithmetic and geometric structures in cryptography

The Particle-In-Fourier (PIF) Approach Applied to Gyrokinetic Simulations

Analytic twists of modular forms and applications

On Short Sums Of Trace Functions