Abstract
Gábor Halász and Pál Turán were the first who proved unconditionally the Density Hypothesis for Riemann’s zeta function in a fixed strip \( c_0 < {\rm Re} s < 1\). They also showed that the Lindelöf Hypothesis implies a surprisingly strong bound on the number of zeros with \( {\rm Re} s \geq c_1 > 3/4\). In the present work we use an alternative approach to prove their result which does not use either Turán’s power sum method or the large sieve.
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The author would like to thank the anonymous referee for valuable remarks.
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To Gábor Halász on the occasion of his 80th birthday
Supported by the National Research Development and Innovation Office, NKFIH, K 119528 and KKP 133819.
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Pintz, J. On the density theorem of Halász and Turán. Acta Math. Hungar. 166, 48–56 (2022). https://doi.org/10.1007/s10474-021-01204-z
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DOI: https://doi.org/10.1007/s10474-021-01204-z