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math.CO2026
Energy Estimation of the Hamming Slice and its Applications
Aniruddha Biswas, Jihun Hwang, Hemanta K. Maji +2
Let , where , and let be the residues whose canonical -digit binary expansion has Hamming weight . We obtain, in par…
math.NT2026
On some results of Korobov and Larcher and Zaremba's conjecture
Ilya D. Shkredov
We prove, in particular, the well--known Zaremba conjecture from the theory of continued fractions for any prime denominator. More precisely, we show, firstly, that under some mild…
math.CO2026
Structure theory of set addition with two operations
Aliaksei Semchankau, Ilya Shkredov
We take the first step toward a structure theory that includes both operations of a ring . More precisely, we prove a series of inverse results for the structure of se…