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Tauberian Theorem and Prime Number Theorem

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#analytic-number-theory
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How can I calculate this hard complex integral?

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#complex-analysis #prime-numbers #analytic-number-theory #riemann-zeta #zeta-functions
54
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In factoring consecutive numbers, how soon do we expect to see the smallest prime not yet seen?

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#analytic-number-theory #prime-factorization
1k
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When does $\pi(x)$ intersect with $x/\log(x)$?

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#number-theory #prime-numbers #analytic-number-theory
214
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Proving Lindelof hypothesis using Phragmen-Lindelof theorem and Riemann Hypothesis

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#analytic-number-theory #riemann-zeta #riemann-hypothesis
269
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Period of a Dirichlet character

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#analytic-number-theory
2k
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If $(a,b)=1$ then there exist positive integers $x$ and $y$ s.t $ax+by=1$.

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#number-theory #analytic-number-theory
294
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Generalizing Dirichlet characters

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#finite-fields #analytic-number-theory #characters
215
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sequence of diophantine approximants of $\pi$

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#real-analysis #sequences-and-series #analytic-number-theory #pi #diophantine-approximation
35
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can we have probabilistic interpretation of $L(1,( \frac{\cdot }{ p}))^{-1}$

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#elementary-number-theory #analytic-number-theory #probabilistic-method
5.1k
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Why are $L$-functions a big deal?

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#complex-analysis #number-theory #analytic-number-theory #modular-forms #automorphic-forms
114
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On a superior limit involving the multiplication formula for the Gamma function and the divisors $d\mid n$ of a positive integer

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#limits #analytic-number-theory #gamma-function #limsup-and-liminf #arithmetic-functions
231
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Chowla's Construction of prime having least quadratic non-residue $\gg \log p$

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#number-theory #analytic-number-theory #quadratic-residues #quadratic-reciprocity
77
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On Dirichlet series and Firoozbakht's conjecture

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#sequences-and-series #convergence-divergence #prime-numbers #analytic-number-theory #dirichlet-series
197
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Help on an application of Dirichlet's theorem for primes in progression

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#number-theory #elementary-number-theory #prime-numbers #analytic-number-theory

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