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math.NT2026
Additive decompositions of multiplicative subgroups via differential identities
Chi Hoi Yip, Albert Cochrane, Semin Yoo
We develop a local-to-global differential framework for additive decomposition problems involving multiplicative subgroups of prime fields. Starting from Hanson--Petridis-type auxi…
math.NT2026
Multiplicative subgroups are not restricted sumsets
Chi Hoi Yip, Semin Yoo
We determine exactly which proper multiplicative subgroups of a prime field can be represented as a restricted sumset of the form $A\mathbin{\widehat{+}} A=\{a+a':a,a'\in A,\ a\ne…
math.NT2026
Extensions of the Carlitz-McConnel and Blokhuis-Sziklai theorems for unions of cyclotomic classes
Maosheng Xiong, Chi Hoi Yip
Let be a prime, let , and let . A celebrated result of Carlitz and McConnel states that if is a proper subgroup of ,…