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arXiv · 1703.00261

A Variant of the Truncated Perron's Formula and Primitive Roots

D. S. Ramana·O. Ramaré
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Abstract

We show under the Generalised Riemann Hypothesis that for every $δ>0$, almost every prime $q$ in $[Q,2Q]$ has the expected of prime primitive roots in the interval $[x,x+x^{\frac{1}2+δ}]$ provided $Q$ is not more than $x^{\frac{2}{3}-ε}$. We obtain this via a variant of the classical truncated Perron's formula for the partial sums of the coefficients of a Dirichlet series.

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D. S. Ramana, O. Ramaré. 2017-03-01. A Variant of the Truncated Perron's Formula and Primitive Roots. https://arxiv.org/abs/1703.00261

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