# Questions tagged [reference-request]

This tag is used if a reference is needed in a paper or textbook on a specific result.

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### Is there an introduction to probability theory from a structuralist/categorical perspective?

The title really is the question, but allow me to explain. I am a pure mathematician working outside of probability theory, but the concepts and techniques of probability theory (in the sense of ...
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### Ways to prove the fundamental theorem of algebra

This seems to be a favorite question everywhere, including Princeton quals. How many ways are there? Please give a new way in each answer, and if possible give reference. I start by giving two: ...
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### Similarities between Post's Problem and Cohen's Forcing

Remark: I have since learned that G.H. Moore addresses this question in the third reference listed at the end of this post, beginning on p. 157 in which he cites a letter from Kreisel to Gödel dated 4/...
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### Hecke equidistribution

For a prime $p\equiv 1\pmod{4}$, we can write $p=a^2+b^2=N(a+bi)$. Therefore $$a+bi=p^{1/2}e^{i\varphi}$$ where $\varphi\in [0,2\pi]$. I know that Hecke proved that $\varphi$ is equidistributed. I ...
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### Riemann zeta function at positive integers and an Appell sequence of polynomials related to fractional calculus

I was exploring some raising and lowering operators related to an infinitesimal generator for fractional integro-derivatives and found an Appell sequence of polynomials, i.e., an infinite sequence of ...
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The Fourier transform of the volume form of the (n-1)-sphere in $\mathbf R^n$ is given by the well-known formula $$\int_{S^{n-1}}e^{i\langle\mathbf a,\mathbf u\rangle}d\sigma(\mathbf u) = (2\pi)^{\nu ... 1answer 1k views ### Obtaining non-normal varieties by pushout In his answer to this MO question, Karl Schwede claimed that every non-normal variety can be obtained by an appropriate pushout diagram, as sketched in that answer. This would give substance to the ... 2answers 3k views ### 3D models of the unfoldings of the hypercube? There are (apparently) 261 distinct unfoldings of the 4D hypercube, a.k.a., the tesseract, into 3D.1 These unfoldings (or "nets") are analogous to the 11 unfoldings of the 3D cube into the plane.2 ... 1answer 2k views ### Points on a sphere Wonder whether any of you know where it was that the following pearl of topology first appeared: Prove that at any instant of time you can find three isothermal points on the surface of the Earth ... 2answers 2k views ### Integer-distance sets Let S be a set of points in \mathbb{R}^d; I am especially interested in d=2. Say that S is an integer-distance set if every pair of points in S is separated by an integer Euclidean distance. ... 2answers 1k views ### Reference request on birational invariance of Chow group of zero cycles of degree zero Let CH_0(X)^0 denote the group of zero cycles of degree zero modulo rational equivalence. I am looking for a reference for the following fact: If X and Y are smooth and projective varieties ... 1answer 2k views ### Dirichlet series expansion of an analytic function Let F(s)=\sum_{n\geq 1}\frac{a_n}{n^s} be a Dirichlet series with (finite) abscissa of absolute convergence \sigma_a. It can be shown that \forall \sigma >\sigma_a:$$\lim_{T\to\infty}\frac{1}...
A few years ago I first read about the marvelous Euler identity: $\sum_{n\in\mathbb{N}}p(n)z^n=\prod_{k\geq1}\frac{1}{1-z^k}$, where $p(n)$ is the number of partitions of $n$ ($p(0)=1$ by convention)...