# Questions tagged [polylogarithms]

For questions about the polylogarithm function, which is a generalization of the natural logarithm.

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### What can this $\int_{0}^{t} (\pi(x)-Li(x)) dx$ tell us about primes distribution?

Many papers I have read which are related to primes distribution only it discussed sign and refinement Bounds of $\pi(x)-Li (x)$ with $\pi(x)$ is a prime counting function and $Li (x)$ is the ...
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### Polylogarithm : reference request for proof of integral representation

On page 494 of the book Integrals and series, volume I : elementary functions, Gordon and Breach, 1986, by A. P. Prudnikov, Y. A. Brychkov, and O.I. Marichev, (perhaps translated from Russian), the ...
127 views

### Simplify the difference of two dilogarithms--as in the logarithmic counterpart

This question--pertaining to the quantum-information-theoretic topic of "bound entanglement"--stems from the question and answer to https://math.stackexchange.com/questions/3464105/if-possible-...
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### Double integral with csch, or single integral with Polylogarithms

For real $a+b\geq 2$, what is the integral of $I(a,b)=\int_0^\infty\int_0^\infty dxdy\frac{x^ay^b}{x+y} \frac{1}{\sinh^2{x}}\frac{1}{\sinh^2{y}}$ I can reduce this double integral to a single ...
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### What is the current fastest method to calculate Lerch's Phi transcendent?

Lerch's Phi transcendent is $$\Phi(z,s,a) = \sum_{k=0}^{\infty} \frac{z^k}{(k+a)^s}$$ I am trying to compute this for the following parameters: $z$ is complex, $|z| \approx 1$ and $|z|$ < 1 (...
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### Is the quantum dilogarithm related in any way to cohomology of quantum groups?

Is the quantum dilogarithm related in any way to cohomology of quantum groups? This question is a bit vague, and I don't have any rigorous justification for such a connection, but let me explain why ...
966 views

### Why is there a unique hyperbolic simplex of largest area?

Why is there a unqiue ideal $n$-simplex in $\mathbb H^n$ with largest volume for $n\geq 3$? For $n=3$, this is a standard calculation, and for larger dimensions is much harder (see Haagerup and ...
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### Is there a simplicial volume definition of Chern Simons invariants?

Suppose we have some compact hyperbolic 3-manifold $M=\Gamma\backslash\mathbb H^3$. Now we know that the hyperbolic volume of $M$ can be defined as (a constant times) the simplicial volume of the ...