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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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On a summation in "Artin's conjecture for primitive roots" by Heath-Brown

This is a question on the paper: D. R. Heath-Brown. Artin's conjecture for primitive roots. Quarterly J. Math. 37 (1): 27–38, 1986. At the beginning of the proof of his main theorem on page 35, Heath- …