New bounds showing that a nontrivial shift of a multiplicative subgroup containing a product set AB has |A||B| essentially bounded by |G|, plus first nontrivial upper bounds on generalized Diophantine tuples over finite fields and progress on a conjecture of Sárközy.
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Multiplicative structure of shifted multiplicative subgroups and its applications to Diophantine tuples
New bounds showing that a nontrivial shift of a multiplicative subgroup containing a product set AB has |A||B| essentially bounded by |G|, plus first nontrivial upper bounds on generalized Diophantine tuples over finite fields and progress on a conjecture of Sárközy.