Average of Hardy’s function at Gram points
نویسندگان
چکیده
Let $Z(t)=\chi ^{-1/2}(1/2+it)\zeta (1/2+it)=e^{i\theta (t)}\zeta (1/2+it)$ be Hardy’s function and $g(n)$ the $n$th Gram point defined by $\theta (g(n))=\pi n$. Titchmarsh proved that $$ \sum _{n \leq N} Z(g(2n)) =2N+O(N^{3/4}\log ^{3/4}N) \
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2021
ISSN: ['0065-1036', '1730-6264']
DOI: https://doi.org/10.4064/aa191103-13-2