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January 1, 2026Forum of Mathematics SigmaOpen Access

A uniform metrical theorem in multiplicative Diophantine approximation

Michael Björklund Reynold Fregoli Alexander Gorodnik

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Key Points

This research aims to understand the distribution of small products related to Diophantine approximation in two-dimensional space.
Analyzing the distribution of products of the form q·‖qx1‖·‖qx2‖.
Setting conditions for parameters a, b, and c based on their growth.
Studying values of q within a specified range.
An asymptotic formula characterizes the count of q satisfying specific constraints.
The findings show the behavior of small values in a multiplicative context.
Results indicate the density of numbers in relation to integer distances.

Implication

This investigation reveals the distribution of products in Diophantine approximation, indicating significant mathematical insights.

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Cite This Study

Björklund et al. (2026) studied this question.

synapsesocial.com/papers/69abc2175af8044f7a4eb5b0 https://doi.org/10.1017/fms.2026.10172

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Keep reading

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1On a Theorem of Legendre on Diophantine Approximation2024
2The Duffin-Schaeffer Conjecture for multiplicative Diophantine approximation2024 · 2 citations
3Effective Results in The Metric Theory of Quantitative Diophantine Approximation2024
4Asymptotic distribution for pairs of linear and quadratic forms at integral vectors2024
5On simultaneous approximation to a real number, its square, and its cube, II2024

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