August 20, 2025Proceedings of the American Mathematical Society

An inverse theorem for generalized arithmetic progression with mild multiplicative property

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The main finding reveals a structural theorem for generalized arithmetic progressions, enhancing understanding of their configurations.
Key evidence indicates this theorem applies to large product sets of two distinct progressions, expanding theoretical applications.
The approach employed is analytical, focusing on proving properties within the realm of set theory and number theory.
The significance highlights potential implications for future research in multiplicative properties and arithmetic sequences.

Implication

The inverse theorem establishes a structural theorem for generalized arithmetic progressions, indicating new insights into their properties.

Abstract

In this paper we prove a structural theorem for generalized arithmetic progressions in F p F_p which contain a large product set of two other progressions.

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Cite This Study

Croot et al. (2025) studied this question.

synapsesocial.com/papers/68af4cd8ad7bf08b1ead63cf https://doi.org/10.1090/proc/17324

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Implication

The inverse theorem establishes a structural theorem for generalized arithmetic progressions, indicating new insights into their properties.

Abstract

In this paper we prove a structural theorem for generalized arithmetic progressions in F p F_p which contain a large product set of two other progressions.

An inverse theorem for generalized arithmetic progression with mild multiplicative property

Key Points

Implication

Abstract

Discussion

Cite This Study

An inverse theorem for generalized arithmetic progression with mild multiplicative property

Key Points

Implication

Abstract

Discussion

Cite This Study

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