56 citations · 490 across the 44 of their papers we have counts for
6 papers · 1 filter
Algebraic trace functions over the primes
Étienne Fouvry, Emmanuel Kowalski, Philippe Michel
We study sums over primes of trace functions of -adic sheaves. Using an extension of our earlier results on algebraic twist of modular forms to the case of Eisenstein series…
An inverse theorem for Gowers norms of trace functions over prime fields
Étienne Fouvry, Emmanuel Kowalski, Philippe Michel
We prove estimates for the Gowers uniformity norms of functions over $\Zz/p\Zz$ which are trace functions of certain -adic sheaves, and establish in particular a strong inver…
Counting sheaves using spherical codes
Étienne Fouvry, Emmanuel Kowalski, 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,…
Sieve in discrete groups, especially sparse
Emmanuel Kowalski
We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.
Algebraic twists of modular forms and Hecke orbits
Étienne Fouvry, Emmanuel Kowalski, Philippe Michel
We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable gen…
Explicit growth and expansion for SL_2
Emmanuel Kowalski
We give explicit versions of Helfgott's Growth Theorem for $\SL_2$, as well as of the Bourgain-Gamburd argument for expansion of Cayley graphs modulo primes of subgroups of $\SL_2(…