Ph. Michel publications

Prepublications – Publications – Slides – Course material – Book Project

   – Dec. 2014: Lecture for the conference “Analysis, Spectra and Number Theory” in honor of P. Sarnak, Princeton.

In preparation

– Elements of applied l-adic cohomology (book)
with E. KOWALSKI and E. FOUVRY. 

– Non-vanishing of twisted $L$-functions


 [60] Bilinear sums of Kloosterman sums and applications.

with  E. KOWALSKI and W. SAWIN. Annals of Mathematics, Vol 186 (2017), no. 2, 413–500.

[59] On moments of twisted L-functions. 

with V. BLOMER, E. KOWALSKI, E. FOUVRY and D. MILICEVIC. American Journal of Mathematics, 139 (2017), no. 3, 707–768.

[58] Some applications of smooth bilinear forms with Kloosterman sums 

with  V. BLOMER, E. KOWALSKI, E. FOUVRY and D. MILICEVIC. Proceedings of the Steklov Institute; special issue for the 125th anniversary of I. M. Vinogradov, 296 (2017), 18–29.

[57] On short sums for trace fonctions 

with E. FOUVRY, E. KOWALSKI, C. S. RAJU, J. RIVAT and K. SOUNDARARAJAN. Annales de l’Institut Fourier, 167 (2017), no. 1, 423-449. 

[56]  Algebraic twists of modular forms and Hecke orbits. 

with E. FOUVRY and E. KOWALSKI, GAFA 25 (2015), no. 2, 580-657.

[55] A study in sums of products,

with E. FOUVRY and E. KOWALSKI, Philosophical Transactions of the Royal Society A 373 (2015).

[54] – On the exponent of  distribution of the ternary divisor function 

with E. FOUVRY and E. KOWALSKI, Mathematika 61 (2015), no. 1, 121-144.

[53] New equidistribution estimates of Zhang type 

with D.H.J. POLYMATH, Algebra and Number Theory 8-9 (2014), 2067–2199

[52] Algebraic trace functions over the primes 

with E. FOUVRY and E. KOWALSKI. Duke Math. Journal 163 (9), 1683-1736 (2014).

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

with E. FOUVRY, E. KOWALSKI and S. GANGULY. Commentarii Mathematici Helvetici (to appear)

[50] Counting sheaves using spherical codes

with E. FOUVRY and E. KOWALSKI. Math. Research Letters, vol 20 (2), 305-323 (2013).

[49] An inverse theorem for Gowers norms of trace functions over prime fields

with E. FOUVRY and E. KOWALSKI. Math. Proc. Cambridge Phil. Soc. (to appear).

[48] Hybrid bounds for automorphic forms on ellipsoids over number fields

with V. BLOMER. Journ. Inst. Math. Jussieu (2013).

[47] Linnik’s ergodic method and the distribution of integral points on spheres.

with J. ELLENBERG et A. VENKATESH. arXiv:1001.0897. Proceedings of the International Math. Colloquium2012 (Tata Institute Mumbay). (to appear.)

[46] –The distribution of periodic torus orbits on homonegeous spaces II: Duke’s theorem for quadratic fields.

with M. EINSIEDLER, E. LINDENSTRAUSS et A. VENKATESH. l’Ens. Math. (to appear.)

[45] Sup-norms of functions on unions of ellipsoids.
  with V. BLOMER. IMRN Vol 2011, no 11 (2011), 4934-4966, doi:10.1093/imrn/rnq280.

[44]The distribution of periodic torus orbits on homogeneous spaces III: Duke’s theorem for cubic fields.
with M. EINSIEDLER, E. LINDENSTRAUSS and A. VENKATESH. Annals of Mathematics 173 (2011), 815–885. ArXiv: math.0708.1113.

[43]Consequences of the Gross/Zagier formulae: Stability of average L-values, subconvexity, and non-vanishing mod p.

with D. Ramakrishnan. Serge Lang memorial volume (to appear). ArXiv:0709.4668.

[42]The subconvexity problem for $GL_2$

with A. VENKATESH. Publ. Math IHES, Vol. 111 (2010). DOI 10.1007/s10240-010-0025-8. ArXiv: math.0903.3591.

[41]The distribution of periodic torus orbits on homonegeous spaces I.

with M. EINSIEDLER, E. LINDENSTRAUSS and A. VENKATESH. Duke Math. Journal, vol. 148, n. 1 (2009), p. 119-174. ArXiv: math.DS/0607815.

[40] Some effective results for $\times a \times b$.

with J. BOURGAIN, E. LINDENSTRAUSS and A. VENKATESH. Erg. Th. Dyn. Sys. (4), 29 (2009), 1705-1722.

[39]Bounds for modular L-functions in the level aspect.

with V. BLOMER and G. HARCOS. Ann. Sci. Ecole Norm. Sup. (4),40 (2007), no. 5, 697–740.

[38] Sur le changement de signe des sommes de Kloosterman.

with E. FOUVRY. Annals of Mathematics 165, 3 (2007), p. 675-715.

[37] The subconvexity problem for Rankin-Selberg L functions and Equidistribution of Heegner points. II.

with G. HARCOS. Inventiones Mathematicae 163, 3 (2006), p. 581-655.

[36] A Burgess-like subconvex bound for twisted L-functions,

with V. BLOMER and G. HARCOS (Appendice 2 de Z. Mao). Forum Mathematicum 19, 1, (2007), p. 61-105.

[35] Analytic number theory and families of automorphic L-functions.

Lecture series at the IAS/Park City Summer Institute,  IAS/Park City Math. Series Vol 12, (2007), p. 179-296.

[34]Heegner points and nonvanishing of Rankin-Selberg L-functions

with A. VENKATESH, Proceedings of the Gauss-Dirichlet conference. Clay Math. Proc., vol. 7, Amer. Math. Soc., Providence, RI, 2007, pp. 169–183.

[33]Equidistribution, L-functions and ergodic theory: on some problems of Yu. V. Linnik.

with A. VENKATESH, International Congress of Mathematicians 2006, Madrid, Volume II, 421-458.

[32] The subconvexity problem for Rankin-Selberg L functions and Equidistribution of Heegner points 

Annals of Mathematics 160.1 (2004), 185-236 .

[31] Pseudorandomness of the sign of Kloosterman’s sums.

with E. FOUVRY, J. RIVAT and A. SARKOZY, J. Aust. Math. Soc. 77 (2004), no. 3, 425–436.

[30] On the complex moments of symmetric power L-functions at s=1,

with J. COGDELL. IMRN 2004:31 (2004) 1561-1617. DOI: 10.1155/S1073792804132455.

[29] Crible Asymptotique and Sommes de Kloosterman

with E. FOUVRY. Proceedings of the Session `Analytic number theory and Diophantine equations’ MPI Bonn 2002. Bonner Mathematische Schriften, Nr. 360, Bonn, 2003.

[S] Samuel Etienne M.

with D. MICHEL. Montpellier, 12 Sept (2003).

[28] Familles de fonctions L de formes automorphes and applications.

Proceedings of the “Journées Arithmétiques de Lille.” Journ. Th. Nombres Bordeaux,  Vol 15, Fasc. 1, (2003), 275-307.

[27] Sommes de modules de sommes d’exponentielles.

with E. FOUVRY, Pacific Journal of Mathematics Vol. 209, No 2 (2003), 261-288.

[26] On the Dimension of the Space of Cusp forms associated to 2-dimensional Galois representations

with A. VENKATESH, IMRN 2002:38 (2002) 2021-2027 .

[25] Répartition des zéros des fonctions L and matrices aléatoires.

Séminaire BOURBAKI, Exp. 887, Mars 2001. Astérisque 282 (2002), 211-248.

[24] A la recherche de petites sommes d’exponentielles.

with E. FOUVRY, Annales de l’Institut Fourier. 52, fasc. 1, p. 47-80 (2002).

[23] Simultaneous non-vanishing of twists of automorphic L functions.

with J. M. VANDERKAM, Compositio Mathematica 134, Vol 2 (2002), 135-191.

[22] On the Rankin-Selberg L functions in the level aspect.

with E. KOWALSKI and J. M. VANDERKAM, Duke Mathematical Journal 114(1) (2002). 123-191.

[21] Zeros of families of Automorphic L-functions close to one.

with E. KOWALSKI, Pacific Journal of  Mathematics 207 (2002), 411-431.

[20] The second moment of the symmetric square L function.

with H. IWANIEC, Annales Academiae Scientiarum Fennicae Math.Vol 26, 2001, 465-482.

[19] Deux Théorèmes de non-annulation de valeurs spéciales de fonctions L,

with E. KOWALSKI Manuscripta Mathematica 104, 1-19 (2001).

[18] Appendice de “ Sur la nature non cyclotomique des poins d’ordre fini des courbes elliptiques ” par L. MEREL,

with E. KOWALSKI. Duke Mathematical Journal 110, (2001), no. 1, 111-119. 

[17] Approximation simultanée de réels par des nombres rationnels and noyau de collision de l’équation de Boltzmann,

with J. SCHNEIDER, Comptes Rendus de l’Académie des Sciences Paris , t. 330, Série I, p. 857-862 (2000).

[16] Mollification of the fourth moment of automorphic L-functions and arithmetic applications. ,

with E. KOWALSKI and J. M. VANDERKAM, Inventiones Mathematicae 142, no. 1, 95-151 (2000).

[15] Non-vanishing of higher derivatives of automorphic L-function.

with E. KOWALSKI and J. M. VANDERKAM, Journal für die Reine und Angewendte Mathematik 526, (2000), 1-34.

[14] Exponential decays for the frequency of the analytic rank of Automorphic L-functions ,

with D. R. HEATH-BROWN, Duke Mathematical Journal 102, (2000), no. 3 475-484.

[13] Non-vanishing of high derivatives of Dirichlet L-functions at the critical point ,

with J. M. VANDERKAM. Journal of Number Theory. 81, 130-148 (2000).

[12] An explicit upper bound for the rank of J0 (q) ,

with E. KOWALSKI, Israel Journal of Mathematics   Vol 120 Part A, 179–204 (2000).

[11] A lower bound for the rank of J0(q) ,

with E. KOWALSKI, Acta Arithmetica 94, (2000) 303-343.

[10] The analytic rank of J0(q) and zeros of automorphic L-functions ,

with E. KOWALSKI, Duke Mathematical Journal 100, (1999), no. 3, 503–542.

[9] Progrès récents du crible and applications (d’après Duke, Fouvry, Friedlander and Iwaniec) ,

Séminaire Bourbaki , Astérisque No. 252 (1998), Exp. No. 842, 4, 185–209.

[8] Sur les zéros des fonctions L des courbes elliptiques sur les corps de fonctions ,

Mathematische Annalen 313, (1999) 359-370.

[7] Sur les points de petite hauteur des courbes modulaires X 0 (N) ,

with E. ULLMO, Inventiones Mathematicae 131, 3. (1998) 645-674.

[6] Sur certaines sommes d’exponentielles sur les nombres premiers ,

with E. FOUVRY, Annales Scientifiques de l’Ecole Normale Supérieure , 4e serie, T. 31, (1998) 93-130.

[5] Minorations de Sommes d’ exponentielles ,

Duke Mathematical Journal 95, (1998), no. 2, 227–240.

[4] Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman II ,

Duke Mathematical Journal 92, (1998) 221-254.

[A] Anna Francoise M.,

with D. MICHEL, Clamart 22 sep (1997)

[3] Rang moyen de familles de variétés abéliennes ,

Journal of Algebraic Geometry 6 (1997), 201-234.

[J] Juliette Louise M. ,

with D. MICHEL, Clamart 17 dec (1995).

[2] Autour de la conjecture de Sato-Tate pour les sommes de Kloosterman I ,

Inventiones Mathematicae 121, (1995) 61-78.

[1] Rang moyen de familles de courbes elliptiques and lois de Sato-Tate ,

Monatshefte fur Mathematik 120, (1995) 127-136.

Course material