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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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asymptotic families of ramanujan near-integers?

This is a follow-up to the question on the Ramanujan constant. Can one find an asymptotic family of shockingly near-integers obtained by raising e to some simple algebraic number, in the spirit of Ra …
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