Some mean value results related to Hardy’s function

Autor: Wenguang Zhai, Xiaodong Cao, Yoshio Tanigawa
Rok vydání: 2021
Předmět:
Zdroj: Research in Number Theory. 7
ISSN: 2363-9555
2522-0160
DOI: 10.1007/s40993-021-00255-z
Popis: Let $$\zeta (s)$$ and Z(t) be the Riemann zeta function and Hardy’s function respectively. We show asymptotic formulas for $$\int _0^T Z(t)\zeta (1/2+it)dt$$ and $$\int _0^T Z^2(t) \zeta (1/2+it)dt$$ . Furthermore we derive an upper bound for $$\int _0^T Z^3(t) \chi ^{\alpha }(1/2+it)dt$$ for $$-1/2
Databáze: OpenAIRE
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