A strengthening of Chang's lemma
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914545049534464 |
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| author | Carenini, Gaia Franchi, Leonardo |
| author_facet | Carenini, Gaia Franchi, Leonardo |
| contents | We prove a strengthening of Chang's lemma for subsets of $\mathbb F_p^n$. The classical conclusion that the large spectrum is contained in a subspace of dimension at most $2\varepsilon^{-2}\log(1/α)$ is refined to show that every character outside this subspace has small correlation with the set not only globally, but also on average over the cosets of the orthogonal complement, in a natural cosetwise $\ell^1$ norm. As a consequence, we obtain a localized counting lemma. We also give an extension of the argument to arbitrary finite abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07916 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A strengthening of Chang's lemma Carenini, Gaia Franchi, Leonardo Number Theory Combinatorics Group Theory We prove a strengthening of Chang's lemma for subsets of $\mathbb F_p^n$. The classical conclusion that the large spectrum is contained in a subspace of dimension at most $2\varepsilon^{-2}\log(1/α)$ is refined to show that every character outside this subspace has small correlation with the set not only globally, but also on average over the cosets of the orthogonal complement, in a natural cosetwise $\ell^1$ norm. As a consequence, we obtain a localized counting lemma. We also give an extension of the argument to arbitrary finite abelian groups. |
| title | A strengthening of Chang's lemma |
| topic | Number Theory Combinatorics Group Theory |
| url | https://arxiv.org/abs/2605.07916 |