Bounds in Cohen's idempotent theorem

Abstract

We show that if $G$ is a finite Abelian group and $f$ is an integer-valued map on $G$ with algebra norm at most $M$ then there is some $L<\exp (M^{4+o(1)})$, cosets of (possibly different) subgroups $W_1,...,W_L$, and $s_1,...,s_L\in \{-1,1\}$ such that $f={\sum }_i{s}_i{1}_{W_i}$.

55pp; corrected arXiv title

References in corpus (3)

• The structure theory of set addition revisited
• Stable arithmetic regularity in the finite-field model
• Boolean functions with small spectral norm, revisited

Cited by in corpus (1)

• Boolean functions with small spectral norm, revisited