Philippe Michel
EPFL SB MATH TAN
MA C3 634 (Bâtiment MA)
Station 8
1015 Lausanne
+41 21 693 25 76
+41 21 693 55 55
Office: MA C3 634
EPFL › SB › MATH › TAN
Site web: https://tan.epfl.ch
+41 21 693 25 76
EPFL › SB › SB-SMA › SMA-ENS
Site web: https://sma.epfl.ch/
+41 21 693 25 76
EPFL › SB › SB-DEC › SB-CEA
+41 21 693 25 76
EPFL › VPA › VPA-AVP-DLE › AVP-DLE-EDOC › EDMA-GE
Site web: https://go.epfl.ch/phd-edma
Prix et distinctions
Collège de France
1999
0
Toroidal families and averages of L-functions, I
Acta Arithmetica. 2024. DOI : 10.4064/aa230323-24-5.The unipotent mixing conjecture
Journal D Analyse Mathematique. 2023. DOI : 10.1007/s11854-023-0326-8.On algebraic twists with composite moduli
Ramanujan Journal. 2023. DOI : 10.1007/s11139-023-00789-z.ALGEBRAIC TWISTS OF GL3 x GL2 L-FUNCTIONS
American Journal Of Mathematics. 2023. DOI : 10.1353/ajm.2023.0015.Algebraic twists of GL(2) automorphic forms
Lausanne, EPFL, 2023. DOI : 10.5075/epfl-thesis-10178.Simultaneous supersingular reductions of CM elliptic curves
Journal Fur Die Reine Und Angewandte Mathematik. 2022. DOI : 10.1515/crelle-2021-0086.Recent Progresses On The Subconvexity Problem
Asterisque. 2022. DOI : 10.24033/ast.1191.Some recents advances on Duke’s equidistribution theorems
2021. Linde Hall Inaugural Math Symposium, Pasadena, United States, 2019-02-22 - 2019-02-24. p. 107 - 132. DOI : 10.1090/pspum/104/01873.Moments of L-functions and exponential sums
Lausanne, EPFL, 2019. DOI : 10.5075/epfl-thesis-7904.Large Sieve Inequalities for Algebraic Trace Functions
International Mathematics Research Notices. 2017. DOI : 10.1093/imrn/rnw074.Bilinear forms with Kloosterman sums and applications
Annals Of Mathematics. 2017. DOI : 10.4007/annals.2017.186.2.2.Some applications of smooth bilinear forms with Kloosterman sums
Proceedings Of The Steklov Institute Of Mathematics. 2017. DOI : 10.1134/S0081543817010023.On Moments Of Twisted L-Functions
American Journal Of Mathematics. 2017. DOI : 10.1353/ajm.2017.0019.Analytic twists of modular forms and applications
Lausanne, EPFL, 2017. DOI : 10.5075/epfl-thesis-7559.On Short Sums Of Trace Functions
Annales De L Institut Fourier. 2017. DOI : 10.5802/aif.3087.Algebraic twists of modular forms and Hecke orbits
Geometric And Functional Analysis. 2015. DOI : 10.1007/s00039-015-0310-2.On The Exponent Of Distribution Of The Ternary Divisor Function
Mathematika. 2015. DOI : 10.1112/S0025579314000096.A study in sums of products
Philosophical Transactions Of The Royal Society A-Mathematical Physical And Engineering Sciences. 2015. DOI : 10.1098/rsta.2014.0309.Algebraic Trace Functions Over The Primes
Duke Mathematical Journal. 2014. DOI : 10.1215/00127094-2690587.Gaussian distribution for the divisor function and Hecke eigenvalues in arithmetic progressions
Commentarii Mathematici Helvetici. 2014. DOI : 10.4171/Cmh/342.An inverse theorem for Gowers norms of trace functions over F-p
Mathematical Proceedings Of The Cambridge Philosophical Society. 2013. DOI : 10.1017/S030500411300025X.Counting Sheaves Using Spherical Codes
Mathematical Research Letters. 2013. DOI : 10.4310/MRL.2013.v20.n2.a8.Hybrid Bounds For Automorphic Forms On Ellipsoids Over Number Fields
Journal Of The Institute Of Mathematics Of Jussieu. 2013. DOI : 10.1017/S1474748012000874.Problème de sous-convexité pour GL2xGL1
Lausanne, EPFL, 2013. DOI : 10.5075/epfl-thesis-5623.Distribution of periodic torus orbits and Duke's theorem for cubic fields
Annals Of Mathematics. 2011. DOI : 10.4007/annals.2011.173.2.5.Sup-norms of Eigenfunctions on Arithmetic Ellipsoids
International Mathematics Research Notices. 2011. DOI : 10.1093/imrn/rnq280.The Subconvexity Problem For Gl(2)
Publications Mathematiques De L Ihes. 2010. DOI : 10.1007/s10240-010-0025-8.The distribution of periodic torus orbits on homogeneous spaces
Duke Mathematical Journal. 2009. DOI : 10.1215/00127094-2009-023.Some effective results for $\times a \times b$
Ergodic Theory and Dynamical Systems. 2009. DOI : 10.1017/S0143385708000898.Heegner points and non-vanishing of Rankin/Selberg $L$-functions.
2007. Analytic number theory. A tribute to Gauss and Dirichlet, Göttingen, Germany, June 20-24, 2005. p. 169 - 183.Analytic number theory and families of automorphic L-functions
Automorphic Forms and Applications; Providence, RI: American Mathematical Society, 2007. p. 179 - 296.Bounds for modular $L$-functions in the level aspect
Annales Scientifiques de l'Ecole Normale Supérieure. 2007. DOI : 10.1016/j.ansens.2007.05.003.A Burgess-like subconvex bound for twisted $L$-functions (Appendix 2 by Z. Mao).
Forum Math.. 2007. DOI : 10.1515/FORUM.2007.003.On the sign change of Kloosterman sums. (Sur le changement de signe des sommes de Kloosterman.)
Annals of Mathematics. 2007. DOI : 10.4007/annals.2007.165.675.The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points. II
Inventiones Mathematicae. 2006. DOI : 10.1007/s00222-005-0468-6.Equidistribution, $L$-functions and ergodic theory: on some problems of Yu. Linnik.
2006. International congress of mathematicians (ICM), Madrid, Spain, August 22-30, 2006. p. 421 - 458.Equidistribution, L-functions and Ergodic Theory: on some problems of Y.V Linnik
Congrès international de Mathématiciens (section Théorie des Nombres), Madrid.On the complex moments of symmetric power $L$-functions at $s = 1$
International Mathematics Research Notices. 2004. DOI : 10.1155/S1073792804132455.Pseudorandomness of the sign of Kloosterman's sums
Journal of the Australian Mathematical Society. 2004. DOI : 10.1017/S1446788700014543.The subconvexity problem for Rankin-Selberg $L$-functions and equidistribution of Heegner points
Annals of Mathematics. 2004. DOI : 10.4007/annals.2004.160.185.On the Shifted Convolution Problem
Workshop on Automorphic L-functions, Toronto, May 5 2003.Families of $L$-functions of automorphic forms and applications. (Familles de fonctions $L$ de formes automorphes et applications.)
Journal de Théorie des Nombres de Bordeaux. 2003.Horizontal vs. Vertical SATO/TATE
Conférence "Arithmetic Geometry and Number Theory" en l'honneur du 60ème anniversaire de Nick Katz, Princeton, December 12 2003.Sums of moduli of exponential sums. (Sommes de modules de sommes d'exponentielles.)
Pacific Journal of Mathematics. 2003. DOI : 10.2140/pjm.2003.209.261.Asymptotic sieve and Kloosterman sums. (Crible asymptotique et sommes de Kloosterman)
2003. Session "analytic number theory and Diophantine equations", Bonn, Germany, January-June, 2002.À la recherche de petites sommes d'exponentielles. (In search of small exponential sums).
Annales de l'Institut Fourier. 2002. DOI : 10.5802/aif.1876.Random Matrix Theory and the distribution of zeros of $L$-functions. (Répartition des zéros des fonctions $L$ et matrices aléatoires.)
Astérisque. 2002.On the dimension of the space of cusp forms associated to 2-dimensional complex Galois representations
International Mathematics Research Notices. 2002. DOI : 10.1155/S1073792802206121.Zeros of families of automorphic $L$-functions close to 1
Pacific Journal of Mathematics. 2002.Simultaneous nonvanishing of twists of automorphic $L$-functions
Compositio Mathematica. 2002. DOI : 10.1023/A:1020544429383.Rankin-Selberg $L$-functions in the level aspect
Duke Mathematical Journal. 2002. DOI : 10.1215/S0012-7094-02-11416-1.Two non-vanishing theorems of special values of $L$-functions. (Deux théorèmes de non-annulation de valeurs spéciales de fonctions $L$.)
Manuscripta Mathematica. 2001. DOI : 10.1007/s002290170043.Appendice de "Sur la nature non-cyclotomique des points d'ordre fini des courbes elliptiques" par L. Merel
Duke Mathematical Journal. 2001.The second moment of the symmetric square $L$-functions
Annales Academiae Scientiarum Fennicae, Mathematica. 2001.Non-vanishing of high derivatives of automorphic $L$-functions at the center of the critical strip
Journal für die Reine und Angewandte Mathematik. 2000. DOI : 10.1515/crll.2000.074.Mollification of the fourth moment of automorphic $L$-functions and arithmetic applications
Inventiones Mathematicae. 2000. DOI : 10.1007/s002220000086.Explicit upper bound for the (analytic) rank of $J_0(q)$
Israel Journal of Mathematics. 2000. DOI : 10.1007/s11856-000-1276-8.Exponential decay in the frequency of analytic ranks of automorphic $L$-functions
Duke Mathematical Journal. 2000. DOI : 10.1215/S0012-7094-00-10235-9.Non-vanishing of high derivatives of Dirichlet $L$-functions at the central point
Journal of Number Theory. 2000. DOI : 10.1006/jnth.1999.2460.Simultaneous approximation of real numbers by rational numbers and its application to the Boltzmann equation. (Approximation simultanée de réels par des nombres rationnels et noyau de collision de l'équation de Boltzmann.)
Comptes Rendus de l'Académie des Sciences. Série 1.. 2000. DOI : 10.1016/S0764-4442(00)00258-5.A lower bound for the rank of $J_0(q)$
Acta arithmetica. 2000.On the zeros of $L$-functions on function fields. (Sur les zéros de fonctions $L$ sur les corps de fonctions.)
Mathematische Annalen. 1999. DOI : 10.1007/s002080050264.The analytic rank of $Jsub 0(q)$ and zeros of automorphic $L$-functions
Duke Mathematical Journal. 1999. DOI : 10.1215/S0012-7094-99-10017-2.Points of small height on the modular curves $X_0(N) $. (Points de petite hauteur sur les courbes modulaires $X_0(N)$.)
Inventiones Mathematicae. 1998. DOI : 10.1007/s002220050216.On some exponential sums over primes. (Sur certaines sommes d'exponentielles sur les nombres premiers.)
Annales Scientifiques de l'Ecole Normale Supérieure, série 4***. 1998.Lower bounds of exponential sums. (Minorations de sommes d'exponentielles.)
Duke Mathematical Journal. 1998. DOI : 10.1215/S0012-7094-98-09507-2.On the Sato-Tate conjecture for Kloosterman sums. II. (Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman. II.)
Duke Mathematical Journal. 1998. DOI : 10.1215/S0012-7094-98-09205-5.Recent progress of the sieve and applications [after Duke, Fouvry, Friedlander, Iwaniec]. (Progrès récents du crible et applications [d'après Duke, Fouvry, Friedlander, Iwaniec].)
Astérisque. 1998.The rank of families of abelian varieties. (Le rang de familles de variétés abéliennes.)
Journal of Algebraic Geometry. 1997.On the Sato-Tate conjecture for Kloosterman sums. (Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman. I.)
Inventiones Mathematicae. 1995. DOI : 10.1007/BF01884290.Average rank of families of elliptic curves and Sato-Tate laws. (Rang moyen de familles de courbes elliptiques et lois de Sato-Tate.)
Monatshefte für Mathematik. 1995. DOI : 10.1007/BF01585913.Enseignement et PhD
Doctorant·es actuel·les
Svenja Zur Verth, Filippo Agostino Vittorio Berta
A dirigé les thèses EPFL de
Han Wu, Alexandre François Peyrot, Raphaël Pierre Zacharias, Vignesh Arumugam Nadarajan
Cours
Advanced analytic number theory
MATH-521
Cette année nous présenterons des applications de la théorie des formes modulaires. Cela pourra inclure: - Equirepartition de points sur la sphere. - Construction de graphes de Ramanujan. - Moyennes invariantes sur la sphere. - Multiplication complexe pour les courbes elliptiques.
Algèbre linéaire avancée I - espaces vectoriels
MATH-110(a)
L'objectif du cours est d'introduire les notions de base de l'algèbre linéaire (pour les futurs mathématiciens) et de démontrer rigoureusement les résultats principaux de ce sujet.
Number theory I.a - Algebraic number theory
MATH-482
La théorie des nombres algébriques est l'étude des propriétés des solutions d'équations polynomiales à coefficients entiers. En partant de problèmes concrets, on introduit ensuite des notions plus générales : corps de nombres, entiers algébriques, unités, les groupes de classes d'idéaux...