most citedThe sum-product conjecture is false for real numbers

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math.NT2026★ 1 cited

The sum-product conjecture is false for real numbers

Thomas F Bloom, Will Sawin, Carl Schildkraut +1

We disprove the sum-product conjecture for real numbers by constructing arbitrarily large (whose elements are algebraic integers in a number field of degree $…

math.NT2026

Odd moments and adding fractions

Thomas F. Bloom, Vivian Kuperberg

We prove near-optimal upper bounds for the odd moments of the distribution of coprime residues in short intervals, confirming a conjecture of Montgomery and Vaughan. As an applicat…