Mathematical Home Page of E. Kowalski

Conferences, research projects,...
♦ During the first semester 2011 (January to June; we like to prepare things well in advance...), P. Michel and myself will organize a special semester "Group actions in number theory: ergodic and analytic methods" at the Centre Interfacultaire Bernoulli of the EPFL Lausanne. More details will be announced in due course...
♦ I was co-organizer of a Spring school and conference at ICTP Trieste on Analytic Number Theory, from April 23 to May 11, 2007. Here is the poster (1.7 MB PDF file) for the school, and its ICTP web page. Pictures and documents related to the school and the proceedings-in-progress are on this page.
♦ Here is the home page of the ARITHMATRICS project.
Links to papers, books,...
♦ Here is a scanned version of a course by N. Katz on Deligne's second proof of the Weil conjectures
♦ Here is my mathematical library. You can check there which books you may borrow...
♦ Here are some unpublished mathematical notes and papers, including the original version of my Ph.D. thesis.
♦ Below are PDF versions of (most of) my published mathematical papers, surveys, books and translation(s). They are listed roughly in reverse chronological order (of writing, not of publication).
Papers, books, translations, surveys
30 Book (to appear) The large sieve and its applications
This is the expanded version of the preprint "The principle of the large sieve" (see arXiv:math.NT/0610021); 233 pages. The general sieve framework developed in this book is also described in a guest post on T. Tao's blog.
29 Book translation Mathematics for physics... and for physicists!
(English translation of «Mathématiques pour la physique... et les physiciens !», by Walter Appel, published by Éditions H&K)
28
 Survey Écarts successifs entre nombres premiers (d'après Goldston, Pintz, Yıldırım)
Séminaire Bourbaki, Exposé 959 (2006).
27 Popular survey Poincaré et la théorie analytique des nombres
(in «L'Héritage scientifique d'Henri Poincaré», edited by É. Charpentier, É. Ghys et A. Lesne)
26 Research paper Exponential sums over definable subsets of finite fields
Also arXiv: math.NT/0504316
25 Research paper Équirépartition adélique de mesures algébriques dans un groupe résoluble et sommes de Kloosterman
24 Research paper On the rank of quadratic twists of elliptic curves over function fields
Also arXiv: math.NT/0503732
23 Research paper Bernstein polynomials and Brownian motion
Also see Problem 11155 in the May, 2005, issue of the Monthly (solution by T. Rivoal). Proposition 6.1 on zeros of random Bernstein polynomials is false! This was pointed out by Johannes Ruf; I was misremembering some properties of zeros of Brownian motion...
22 Research paper
(Crelle, 2006)
The large sieve, monodromy and zeta functions of curves
Also arXiv: math.NT/0503714. Here are a few small corrections (also contained in the forthcoming book "The large sieve and its applications").
21 Research paper Weil numbers generated by other Weil numbers and torsion fields of abelian varieties
Also arXiv: math.NT/0504042
20 Research paper Variations of recognition problems for modular forms
19 Book Analytic Number Theory, with H. Iwaniec
See also the Current list of corrections and (forthcoming) Supplementary material.
18 Survey Elliptic curves, rank in families and random matrices
(Typed version of a survey lecture given at the Newton Institute Workshop and random matrices and L-functions in July 2004, together with a survey lecture on the variation of the rank of elliptic curves in families at the AIM/Princeton University workshop on the Birch and Swinnerton-Dyer Conjecture in November 2003)
17 Research paper Small gaps in coefficients of L-functions and B-free numbers in short intervals, with O. Robert and J. Wu
Also arXiv: math.NT/0507001
16 Research note On the reducibility of arctangents of integers
See also Sequence A002312 in the Encyclopedia of Integer Sequences. (This is a short application of the result of Duke, Friedlander and Iwaniec proved in the graduate course below).
15 Book Un cours de théorie analytique des nombres
(DEA/graduate course in Bordeaux, 2001-2002).
14 Book chapters
(Birkhäuser, 2003)
Automorphic forms, L-functions and number theory: 3 lectures
See some corrections to the published version.
13 Research paper (to appear) Dependency on the group in automorphic Sobolev inequalities
12 Research paper Some Local-Global Applications of Kummer Theory
Note that Proposition 6.11 is not in the published version
11 Research paper
(Pacific J. Math., 2002).
Zeros of families of automorphic L-functions close to 1, with P. Michel
10 Research paper Analytic problems for elliptic curves
Also arXiv: math.NT/0510197
9 Research paper
(Duke Math. J., 2002)
Rankin-Selberg L-functions in the level aspect, with P. Michel and J. Vanderkam
8 Research paper
(Invent. math., 2000)
Mollification of the fourth moment of automorphic L-functions and arithmetic applications, with P. Michel and J. Vanderkam
7 Published
(Israel J. Math., 2000)
Explicit upper bound for the (analytic) rank of J0(q), with P. Michel
6 Research paper Deux théorèmes de non-annulation de valeurs spéciales de fonctions L, with P. Michel
5 Appendix
(Duke Math. J., 2001)
Vérification de l'hypothèse Hp(chi) pour p grand, with P. Michel
Appendix to a paper by L. Merel
4 Research paper
(Crelle, 2000)
Non-vanishing of high derivatives of automorphic L-functions at the center of the critical strip, with P. Michel and J. Vanderkam
3 Research paper
(Acta Arith., 2000)
A lower bound for the rank of J0(q), with P. Michel
2 Research paper
(Duke Math. J., 2000)
The analytic rank of J0(q) and zeros of automorphic L-functions, with P. Michel
1 Research paper<
(Invent. math., 2000)
 A problem of Linnik for elliptic curves and mean value estimates for automorphic representations, with W. Duke and D. Ramakrishnan