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If $\lim_{x\to \infty} f^{(k)}(x)=\theta$ (irrational), then $(f(n))$ is uniformly distributed modulo $1$

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#sequences-and-series #analysis #analytic-number-theory #ergodic-theory #equidistribution
38
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The original function of the following series?

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#sequences-and-series #analysis #taylor-expansion #power-series #analytic-number-theory
476
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Closed-form of $\int_0^\infty \frac{t^s}{(e^t-1)^z}dt$

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#integration #complex-analysis #analytic-number-theory
84
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If the series $\sum f(n) n^{-s}$ converges absolutely for $\sigma > \sigma_a$ and has sum $F(s),$ prove that $F(s) \neq 0$

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#number-theory #analytic-number-theory
49
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Characterization of Möbius-monotonicity

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#analytic-number-theory #arithmetic-functions #mobius-function #mobius-inversion #dirichlet-convolution
105
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Computing the constant in BSD conjecture

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#number-theory #analytic-number-theory #elliptic-curves
78
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Sum versus product on Primes

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#limits #number-theory #exponential-function #analytic-number-theory #euler-mascheroni-constant
104
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an inequality involving the zeta function and its derivative

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#complex-analysis #analytic-number-theory #riemann-zeta #zeta-functions
41
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Minimising an expression involving prime numbers.

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#prime-numbers #analytic-number-theory #discrete-optimization #coprime #combinatorial-number-theory
104
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The mean square of $d_k(n)$

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#number-theory #analytic-number-theory #complex-integration #divisor-sum #multiplicative-function
129
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How is the Zeta function a "generating function"

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#generating-functions #analytic-number-theory #riemann-zeta
268
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Optimal bounds for the product of the divisor function $d(n)$ in short intervals

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#number-theory #prime-numbers #analytic-number-theory #limsup-and-liminf #divisor-counting-function
227
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Zero-free region for the zeta function

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#complex-analysis #analytic-number-theory #gamma-function #riemann-zeta #zeta-functions
57
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Upper bound of prime counter function

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#number-theory #solution-verification #analytic-number-theory
134
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Turán proof that constant sign of Liouville function implies RH

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#analytic-number-theory #riemann-zeta #dirichlet-series #riemann-hypothesis #liouville-function

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