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math.NT2026
Remarks on the inverse Littlewood conjecture
Thomas F. Bloom, Ben Green
The Littlewood conjecture, proven by Konyagin and McGehee-Pigno-Smith in the 1980s, states that if is a finite set of integers with then $\…
math.NT2026
More on the sum-product problem for integers with few prime factors
Rishika Agrawal, Thomas F. Bloom, Giorgis Petridis
We show that if is a finite set of integers in which every integer is divisible by many primes then \[\max(\lvert A+A\rvert,\lvert AA\rvert) \geq \lver…