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Understanding a famous proof by Jitsuro Nagura: Need help understanding one step in the main theorem

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#number-theory #inequality #prime-numbers #logarithms #chebyshev-function
777
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Looking for help understanding the Möbius Inversion Formula

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#number-theory #chebyshev-function #mobius-inversion
138
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Looking for help in understanding Jitsuro Nagura's analysis of the upper bound for $\psi(x)$

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#number-theory #logarithms #gamma-function #chebyshev-function
186
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Generalizing Jitsuro Nagura's result: my resulting upper bound for the second chebyshev function is too low. What am I doing wrong?

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#number-theory #logarithms #factorial #gamma-function #chebyshev-function
378
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Can the Möbius inversion formula be applied to the second Chebyshev function?

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#analytic-number-theory #chebyshev-function #mobius-inversion
149
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Trying to show that $\ln(x!) - \ln(\lfloor\frac{x}{2}\rfloor!) - \ln(\lfloor\frac{x}{3}\rfloor!) - \ln(\lfloor\frac{x}{6}\rfloor!) \ge \psi(x)$

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#number-theory #logarithms #factorial #chebyshev-function
221
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Trying to understand Theorem 2.27 in a recent paper on the Chebyshev function

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#number-theory #inequality #analytic-number-theory #chebyshev-function
134
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The quality of specific triples based on the first $2n$ prime numbers

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#prime-numbers #asymptotics #analytic-number-theory #chebyshev-function
203
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Proof of increasing positive valued function

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#probability #chebyshev-function
334
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Big O and Asymptotic Notation

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#real-analysis #limits #asymptotics #analytic-number-theory #chebyshev-function
119
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Question regarding Chebyshev function bound with product

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#number-theory #chebyshev-function
91
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Lower bound for the limit of a ratio related to the distribution of primes.

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#prime-numbers #analytic-number-theory #chebyshev-function
94
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Is $\sum_{\rho}\frac{x^{\rho+1}}{\rho\left(\rho+1\right)}$ differentiable term by term?

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#calculus #sequences-and-series #complex-analysis #riemann-zeta #chebyshev-function
1.2k
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How would I use Chebyshev's inequality for this problem?

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#statistics #chebyshev-function
540
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Gauss - Chebyshev Quadrature confusion. Please help.

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#numerical-methods #chebyshev-function #quadrature

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