G.H.Hardy proved that zeta function have infinite root that is 1/2+bi. I tried to find the paper including the proof but I couldn’t. Is there anyone who have the paper and can share it?
2026-03-31 18:34:43.1774982083
Hardy’s work about zeta function
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Titchmarsh book. He reports on Hardy (1914) in section 10.2, pages 256-258, pdf 133-134:
https://sites.math.rutgers.edu/~zeilberg/EM18/TitchmarshZeta.pdf
Apparently the first proof of infinitely many zeros on the critical line:
Hardy 1914, pages 1012 - 1014
https://archive.org/details/ComptesRendusAcademieDesSciences0158/page/n1013/mode/2up?view=theater
Hardy writes that he had an earlier announcement in the Proceedings of the London Mathematical Society, in 1914 and, I guess, presented to the Society on 12 March. They do archive the Proceedings but I haven't yet found the exact spot.
1917 or 1918:
https://projecteuclid.org/journalArticle/Download?urlId=10.1007%2FBF02422942
1921:
https://gdz.sub.uni-goettingen.de/id/PPN266833020_0010?tify=%7B%22view%22:%22info%22,%22pages%22:%5B293%5D%7D
..
1914 again: