how to write research about Riemann zeta function

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I read these

1-introduction to analytic number theory by Tom M.Apostol 2-the prime number theorem by G.J.O.Jameson
3-the distribution of prime numbers by A.E.Ingham
4-the paper "Special Values of the Polygamy Functions" by M.RAM MUTRY
5-the paper improved explicit estimate for zeta function" in 2022 by A.Hairy, Patel, and Yang
6- the paper 'Estimate for zeta function" in 2002 by Y.F.Cheng and S.W.Graham I also read other books, articles, and papers but when I read these I read every single word in them

I want to write a research about Riemann zeta function

So do you think now should I read more books and old papers ?or should I try to write a paper and connect with researchers?