English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We give improved bounds for our theorem in [W. T. Gowers and J. Wolf, The true complexity of a system of linear equations.  Proc. London Math. Soc.  (3)  100  (2010), 155–176], which shows that a system of linear forms onF  p  nwith squares that are linearly independent has the expected number of solutions in any linearly uniform subset ofF  p  n    . While in [W. T. Gowers and J. Wolf, The true complexity of a system of linear equations.  Proc. London Math. Soc.  (3)  100  (2010), 155–176] the dependence between the uniformity of the set and the resulting error in the average over the linear system was of tower type, we now obtain a doubly exponential relation between the two parameters. Instead of the structure theorem for bounded functions due to Green and Tao [An inverse theorem for the Gowers  U  3 (G) norm.  Proc. Edinb. Math. Soc.  (2)  51  (2008), 73–153], we use the Hahn–Banach theorem to decompose the function into a quadratically structured plus a quadratically uniform part. This new decomposition makes more efficient use of the  U  3  inverse theorem [B. J. Green and T. Tao, An inverse theorem for the Gowers  U  3 (G) norm.  Proc. Edinb. Math. Soc.  (2)  51  (2008), 73–153].

LINEAR FORMS AND QUADRATIC UNIFORMITY FOR FUNCTIONS ON F p n