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How to improve Chebyshev bound on the prime counting inequality?

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#number-theory #prime-gaps #chebyshev-function
115
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Minimization of Maximum Eigenvalue Error for Richardson Extrapolation

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#proof-writing #numerical-methods #problem-solving #fixed-point-iteration #chebyshev-function
36
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Using balanced multi-sets to estimate Chesbyschev's function $\psi(x)$

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#number-theory #prime-numbers #estimation #chebyshev-function
108
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An inequality on a function of Chebyshev

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#inequality #prime-numbers #chebyshev-function
74
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How to relate the two versions of Bombieri-Vinogradov theorem to one another?

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#number-theory #prime-numbers #sieve-theory #chebyshev-function
78
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How is it proved that $\sum_{p\le x}\frac1p=\int_2^x\frac{d(\vartheta(t))}{t\log t}$?

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#real-analysis #number-theory #definite-integrals #prime-numbers #chebyshev-function
463
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The asymptotic of the first Chebyshev function, using the Prime Number Theorem

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#number-theory #prime-numbers #asymptotics #chebyshev-function
54
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$\sum_{p,m\geq 3}(-1)^{m(p-1)/2}e^{-p^my}\log p = O(y^{-1/3})$

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#prime-numbers #analytic-number-theory #chebyshev-function #summation-by-parts
176
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Approximating $\vartheta(x)=\sum_{p\le x} \log(p)?$

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#number-theory #prime-numbers #approximation #chebyshev-function
116
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Proving the first Chebyshev function $\vartheta(x)=O(x)$ using prime factorisation of ${2n \choose n}$

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#number-theory #prime-numbers #analytic-number-theory #prime-factorization #chebyshev-function
138
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How can we prove $\sum_{p\leq x}\ln(p) < 2x$?

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#number-theory #analytic-number-theory #chebyshev-function
223
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Establish an upper bound for $\zeta'(s)\over\zeta(s)$?

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#complex-analysis #analytic-number-theory #complex-integration #upper-lower-bounds #chebyshev-function
79
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Correct reasoning for a finite number of twin primes next to the lcm of first N numbers?

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#prime-numbers #gcd-and-lcm #twin-primes #chebyshev-function
393
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Is there a random variable $X$ for which $P [µx - 2σ ≤ X ≤ µx + 2σx] = 0.6$?

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#probability #chebyshev-function
193
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Chebyshev’s $\theta_1(x) = \sum_{n \leqslant x } (x-n) \Lambda_1 (n)$

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#number-theory #prime-numbers #analytic-number-theory #chebyshev-function

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