Chebyshev's Bias for Ramanujan's $τ$ -function via the Deep Riemann Hypothesis

preprint2022arXivOpen access

The authors assume the Deep Riemann Hypothesis to prove that a weighted sum of Ramanujan's $τ$ -function has a bias to being positive. This phenomenon is an analogue of Chebyshev's bias.

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Chebyshev's Bias for Ramanujan's $τ$ -function via the Deep Riemann Hypothesis

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Chebyshev's Bias for Ramanujan's τττ-function via the Deep Riemann Hypothesis

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Chebyshev's Bias for Ramanujan's $τ$ -function via the Deep Riemann Hypothesis