A Note on the Linnik's constant

Details A Note on the Linnik's constant A Note on the Linnik's constant

2010-10-18

arxiv.org/abs/1010.3544v1

Mathematics

Number Theory

Scientific paper

Let $P(a,q)$ be the least prime in the arithmetic progression $\{n\equiv
a(mod\ q)\}$. In this note, when $q$ has bounded cubic part and $(a,q)=1$, we
combine the Heath-Brown's method and the Burgess's bounds for L-functions to
obtain $ P(a,q)\ll q^{4.5}.$

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