Resolves Erdős-Straus, Erdős, and Erdős-Pomerance-Sárközy conjectures on prime factors of consecutive integers via probabilistic method and quantitative correlations.
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2025 2verdicts
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Proves asymptotics for integral rational points on a family of degree-one del Pezzo surfaces by reducing the count to correlation sums of binary quadratic and quartic representation numbers analyzed via modular forms.
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Quantitative correlations and some problems on prime factors of consecutive integers
Resolves Erdős-Straus, Erdős, and Erdős-Pomerance-Sárközy conjectures on prime factors of consecutive integers via probabilistic method and quantitative correlations.
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Counting points on a family of degree one del Pezzo surfaces
Proves asymptotics for integral rational points on a family of degree-one del Pezzo surfaces by reducing the count to correlation sums of binary quadratic and quartic representation numbers analyzed via modular forms.