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math.NT2026
Uniform sum-product phenomenon for algebraic groups and Bremner's conjecture
Joseph Harrison, Akshat Mudgal, Harry Schmidt
In this paper we combine methods from additive combinatorics and Diophantine geometry to study the generalised sum-product phenomenon in algebraic groups. As an application of this…
math.NT2025
Additive relations in irrational powers
Joseph Harrison
We investigate the interaction between raising to an irrational power and addition of real numbers. Thus, for a finite set of non-negative real numbers, let $A^{[c]} = \{a^c :…