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The Prouhet--Tarry--Escott problem for subsets with small doubling in integral domains
Ernie Croot, Junzhe Mao, Chi Hoi Yip
The Prouhet--Tarry--Escott (PTE) problem has many generalizations and has been studied in various algebraic domains. In this paper, we prove that finite subsets of integral dom…
Positivity preservers over finite fields II
Dominique Guillot, Himanshu Gupta, Prateek Kumar Vishwakarma +1
We say that a matrix over a finite field is positive definite if it is symmetric and each of its leading principal minors is a nonzero square in . In p…
A sharp inverse theorem for the quadratic large sieve
Ernie Croot, Chi Hoi Yip, Junzhe Mao +1
We prove that if , , and for every prime , then contains at least el…
An absolute bound for generalized Diophantine tuples over polynomial rings
Kin Ming Tsang, Chi Hoi Yip
Let be an algebraically closed field of characteristic . Let be an integer, and let . We study generalized Diophantine tup…
A combinatorial large sieve for Sidon sets, distances, and norm forms
Ernie Croot, Junzhe Mao, Cosmin Pohoata +2
We develop a new combinatorial large sieve method for sets with bounded algebraic multiplicities. The method exploits algebraic splitting modulo many small primes: local congruence…
Hilbert cubes in sets with arithmetic properties
Ernie Croot, Junzhe Mao, Chi Hoi Yip
In this paper, we introduce new general frameworks for estimating the maximal dimension of Hilbert cubes contained in finite truncations of arbitrary sets. As applications, we inve…