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Philippe Michel

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Related publications (25)

Page 1 of 2

Sup-norms of Eigenfunctions on Arithmetic Ellipsoids

Philippe Michel

Let B be a positive quaternion algebra, and let O subset of B be an Eichler order. There is associated, in a natural way, a variety X = X(O) the connected components of which are indexed by the ideal classes of O and are isomorphic to spheres. This variety ...

Oxford University Press2011

Recent Progresses On The Subconvexity Problem

Philippe Michel

The subconvexity problem aims at providing non-trivial (i.e. subconvex) bounds for central values of automorphic L-functions; the main conjecture in this area is the Generalized Lindelof Hypothesis which itself is a consequence of the Generalized Riemann H ...

2022

Bilinear forms with Kloosterman sums and applications

Philippe Michel

We prove nontrivial bounds for general bilinear forms in hyper-Kloosterman sums when the sizes of both variables may be below the range controlled by Fourier-analytic methods (Polya-Vinogradov range). We then derive applications to the second moment of cus ...

Annal Mathematics2017

Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields

Philippe Michel

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

Distribution of periodic torus orbits and Duke's theorem for cubic fields

Philippe Michel

We study periodic torus orbits on spaces of lattices. Using the action of the group of adelic points of the underlying tori, we define a natural equivalence relation on these orbits, and show that the equivalence classes become uniformly distributed. This ...

2011

On Short Sums Of Trace Functions

Chandra Sekhar Raju, Philippe Michel

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 Subconvexity Problem For Gl(2)

Philippe Michel

Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL(1) and GL(2) automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our ...

Springer-Verlag2010

Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions

Philippe Michel

We show that, in a restricted range, the divisor function of integers in residue classes modulo a prime follows a Gaussian distribution, and a similar result for Hecke eigenvalues of classical holomorphic cusp forms. Furthermore, we obtain the joint distri ...

European Mathematical Soc2014

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

Some recents advances on Duke’s equidistribution theorems

Philippe Michel

Duke’s theorems are three equidistribution statements for sets of representations of large integers by ternary quadratic forms. In this paper we survey some recent development of these beautiful theorems. ...

American Mathematical Society2021

Counting Sheaves Using Spherical Codes

Philippe Michel

Using the Riemann Hypothesis over finite fields and bounds for the size of spherical codes, we give explicit upper bounds, of polynomial size with respect to the size of the field, for the number of geometric isomorphism classes of geometrically irreducibl ...

International Press2013

On The Exponent Of Distribution Of The Ternary Divisor Function

Philippe Michel

We show that the exponent of distribution of the ternary divisor function d(3) in arithmetic progressions to prime moduli is at least 1/2 + 1/46, improving results of Friedlander-Iwaniec and Heath-Brown. Furthermore, when averaging over a fixed residue cla ...

London Mathematical Society, Cambridge2015

Toroidal families and averages of L-functions, I

Philippe Michel

We initiate the study of certain families of L-functions attached to characters of subgroups of higher-rank tori, and of their average at the central point. In particular, we evaluate the average of the values L( 2 1 , chi a )L( 21 , chi b ) for arbitrary ...

Polish Acad Sciences Inst Mathematics-Impan2024

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

The distribution of periodic torus orbits on homogeneous spaces

Philippe Michel

2009

A study in sums of products

Philippe Michel

We give a general version of cancellation in exponential sums that arise as sums of products of trace functions satisfying a suitable independence condition related to the Goursat-Kolchin-Ribet criterion, in a form that is easily applicable in analytic num ...

Royal Society, The2015

ALGEBRAIC TWISTS OF GL3 x GL2 L-FUNCTIONS

Philippe Michel, Yongxiao Lin

We prove that the coefficients of a GL3 x GL2 Rankin-Selberg L-function do not correlate with a wide class of trace functions of small conductor modulo primes, generalizing the corresponding result of Fouvry, Kowalski, and Michel for GL2 and of Kowalski, L ...

Johns Hopkins Univ Press2023

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

Rankin-Selberg coefficients in large arithmetic progressions

Philippe Michel, Yongxiao Lin

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

Some effective results for $\times a \times b$

Philippe Michel

2009