Erdős-Graham conjecture on binomial divisors holds for large k but fails for small k via restricted coverings and sieves.
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Resolves Erdős-Straus, Erdős, and Erdős-Pomerance-Sárközy conjectures on prime factors of consecutive integers via probabilistic method and quantitative correlations.
Establishes best known uniform bounds on newform correlation and decorrelation integrals, yielding effective holomorphic QUE and extending prior decorrelation results via refined weak subconvexity for Rankin-Selberg L-functions.
citing papers explorer
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Binomial coefficients with divisors avoiding an interval
Erdős-Graham conjecture on binomial divisors holds for large k but fails for small k via restricted coverings and sieves.
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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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Effective correlation and decorrelation for newforms, and weak subconvexity for $L$-functions
Establishes best known uniform bounds on newform correlation and decorrelation integrals, yielding effective holomorphic QUE and extending prior decorrelation results via refined weak subconvexity for Rankin-Selberg L-functions.