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arXiv · 2601.08810

The Jamneshan-Tao conjecture for finite abelian groups of bounded rank

Pablo Candela·Diego González-Sánchez·Balázs Szegedy
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Abstract

We confirm the Jamneshan-Tao conjecture for finite abelian groups of rank at most a fixed integer $R$ (i.e. finite abelian groups generated by at most $R$ elements), by proving an inverse theorem for 1-bounded functions of non-trivial Gowers norm on such groups, concluding that such a function must correlate non-trivially with a nilsequence of bounded complexity.

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Pablo Candela, Diego González-Sánchez, Balázs Szegedy. 2026-01-13. The Jamneshan-Tao conjecture for finite abelian groups of bounded rank. https://arxiv.org/abs/2601.08810

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