12 papers
Additive decompositions of multiplicative subgroups in prime fields: a self-contained approach
Chi Hoi Yip, Semin Yoo
Sárközy conjectured that the nonzero quadratic residues modulo a sufficiently large prime have no nontrivial additive decomposition. Hanson and Petridis proved the conjecture for…
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…
Multiplicative irreducibility of shifted multiplicative subgroups in the extremal case
Semin Yoo
In a recent breakthrough, Kalmynin proved a conjecture of Sárközy on additive irreducibility of the set of quadratic residues in a prime field. More recently, Kim, Yip, and Yoo i…
-Diophantine sets over finite fields via quasi-random hypergraphs from multivariate polynomials
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
We investigate -Diophantine sets over finite fields via new explicit constructions of families of quasi-random hypergraphs from multivariate polynomials. In particular, our cons…
Multiplicative irreducibility of shifted multiplicative subgroups
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
In a recent breakthrough, Kalmynin resolved conjectures of Lev--Sonn and Sárközy on additive decompositions of multiplicative subgroups of prime fields. In this paper, inspired by…
Product representations of polynomials over finite fields
Hyunwoo Lee, Chi Hoi Yip, Semin Yoo
Erdős, Sárközy, and Sós studied the asymptotics of the maximum size of a subset of such that it does not contain distinct elements whose product is a perfec…