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$p$ is adherent value of $\left(\sum_{i=1}^{p} z_{i}^n\right)_{n\in\mathbb{N}}$ where $z_{i}$ are complex of modulus 1

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#sequences-and-series #diophantine-approximation
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Prove $\sum_{n=1}^\infty\frac{\cot(\pi n\sqrt{61})}{n^3}=-\frac{16793\pi^3}{45660\sqrt{61}}$

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#sequences-and-series #complex-analysis #number-theory #continued-fractions #diophantine-approximation
123
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Equidistribution of $\{p_n^2 \alpha \}$

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#number-theory #ergodic-theory #diophantine-approximation #equidistribution
47
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Diophantine Approximation on Quadratic Polynomials

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#number-theory #approximation #diophantine-approximation
188
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Bad approximation, alternative definiton

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#number-theory #analytic-number-theory #diophantine-approximation
64
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Exercise 1.12 from Ed Burger's book The Number Jungle.

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#diophantine-approximation
131
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What is sum of squared elements of Farey sequence?

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#number-theory #analytic-number-theory #diophantine-approximation #farey-sequences
404
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What is $T^1(\mathbb H^2/PSL_2(\mathbb Z))$?

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#riemannian-geometry #hyperbolic-geometry #ergodic-theory #diophantine-approximation
37
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Existence of interesting infinite subsets of the rationals whose elements are not arbitrarily close to some reals

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#real-analysis #diophantine-approximation
656
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A variant of Kronecker's approximation theorem?

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#real-analysis #sequences-and-series #approximation #real-numbers #diophantine-approximation
309
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Quasi-periodic sequence

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#sequences-and-series #fourier-series #irrational-numbers #diophantine-approximation #almost-periodic-functions
402
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An Engineer sets out to Prove Fermat's Last Theorem ...

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#number-theory #diophantine-equations #analytic-number-theory #diophantine-approximation
1.1k
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Examples of transcendental functions giving almost integers

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#real-analysis #numerical-methods #approximation-theory #diophantine-approximation
189
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Citable reference (book) for a variant of Kronecker's Approximation Theorem

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#reference-request #approximation #diophantine-approximation
230
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Inequality $|\cos(k)| \geq \frac{1}{2^k}$ for $k\geq 0$

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#inequality #diophantine-approximation

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