## An inverse theorem for Gowers norms of trace functions over F-p

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.

Published in:
Mathematical Proceedings Of The Cambridge Philosophical Society, 155, 2, 277-295
Year:
2013
Publisher:
New York, Cambridge Univ Press
ISSN:
0305-0041
Laboratories: