5 citations · 24 across the 23 of their papers we have counts for
15 papers · 1 filter
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…
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…
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 ,…
Bipartite Diophantine tuples and their applications
Kin Ming Tsang, Chi Hoi Yip
This paper investigates bipartite variants of generalized Diophantine tuples and their applications. We generalize a result of Bugeaud--Dujella on a special family of bipartite Dio…
Multiplicative irreducibility of small perturbations of the set of shifted -th powers
Chi Hoi Yip
Motivated by a conjecture of Erdős on the additive irreducibility of small perturbations of the set of squares, recently Hajdu and Sárközy studied a multiplicative analogue of the…
Oscillation results for the summatory functions of fake mu's
Greg Martin, Chi Hoi Yip
Mossinghoff, Trudgian, and the first author~\cite{MMT23} recently introduced a family of arithmetic functions called ``fake 's'', which are multiplicative functions for which th…
-Diophantine sets over finite fields
Chi Hoi Yip, Semin Yoo
Let , be an odd prime power, and be a polynomial. An -Diophantine set over a finite field is a set $A \subset…
On cyclotomic matrices involving Gauss sums over finite fields
Hai-Liang Wu, Jie Li, Li-Yuan Wang +1
Inspired by the works of L. Carlitz and Z.-W. Sun on cyclotomic matrices, in this paper, we investigate certain cyclotomic matrices involving Gauss sums over finite fields, which c…
Explicit constructions of Diophantine tuples over finite fields
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
A Diophantine -tuple over a finite field is a set of distinct elements in such that is a square in $…
Distribution of power residues over shifted subfields and maximal cliques in generalized Paley graphs
Greg Martin, Chi Hoi Yip
We derive an asymptotic formula for the number of solutions in a given subfield to certain system of equations over finite fields. As an application, we construct new families of m…
Multiplicatively reducible subsets of shifted perfect -th powers and bipartite Diophantine tuples
Chi Hoi Yip
Recently, Hajdu and Sárközy studied the multiplicative decompositions of polynomial sequences. In particular, they showed that when , each infinite subset of $\{x^k+1: x…
Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples
Seoyoung Kim, Chi Hoi Yip, Semin Yoo
In this paper, we investigate the multiplicative structure of a shifted multiplicative subgroup and its connections with additive combinatorics and the theory of Diophantine equati…
An annotated bibliography for comparative prime number theory
Greg Martin, Pu Justin Scarfy Yang, Aram Bahrini +9
The goal of this annotated bibliography is to record every publication on the topic of comparative prime number theory (through mid-2024) together with a summary of its results. We…
Additive decompositions of large multiplicative subgroups in finite fields
Chi Hoi Yip
We show that a large multiplicative subgroup of a finite field cannot be decomposed into or nontrivially. We also find new families of multiplicative s…
Asymptotics for the number of directions determined by in
Greg Martin, Ethan Patrick White, Chi Hoi Yip
Let be a prime and a positive integer such that . For any arithmetic progression of length in , we establish…