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An inverse theorem for Gowers norms of trace functions over Fp

Published online by Cambridge University Press:  25 April 2013

ÉTIENNE FOUVRY ,
EMMANUEL KOWALSKI  and
PHILIPPE MICHEL
ÉTIENNE FOUVRY
Affiliation:
Université Paris Sud, Laboratoire de Mathématique, Campus d'Orsay, 91405 Orsay Cedex, France. e-mail: etienne.fouvry@math.u-psud.fr
EMMANUEL KOWALSKI
Affiliation:
ETH Zürich – D-MATH, Rämistrasse 101, 8092 Zürich, Switzerland. e-mail: kowalski@math.ethz.ch
PHILIPPE MICHEL
Affiliation:
EPFL/SB/IMB/TAN, Station 8, CH-1015 Lausanne, Switzerland. e-mail: philippe.michel@epfl.ch
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Abstract

We study the Gowers uniformity norms of functions over Z/pZ which are trace functions of ℓ-adic sheaves. On the one hand, we establish a strong inverse theorem for these functions, and on the other hand this gives many explicit examples of functions with Gowers norms of size comparable to that of “random” functions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 2 , September 2013 , pp. 277 - 295
Copyright
Copyright © Cambridge Philosophical Society 2013 

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