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Two projection operators may not be commutative, with an explicit example.
A projection operator is a linear mapping from a linear space X to X that then s…
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分析中很多问题都可以用取平均来解决，但是能用取平均解决的问题，本质上是trivial的。 Lonely Runner conjecture本质上是一个不能用取平…
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The Ramanujan-Nagell Theorem: Understanding the Proof
The Ramanujan-Nagell Theorem: Understanding the Proof
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A crash introduction to BSD conjecture
The pdf version is A crash introduction to BSD conjecture . We begin with the We…
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SL_2(Z) and its congruence subgroups
The pdf version is A crash introduction to BSD conjecture . We begin w…
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Dirichlet hyperbola method
A pdf version is Dirichlet hyperbola method. 1. Introduction Theorem 1 $\display…
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Diophantine approximation
I explain some general ideal in the theory of diophantine approximation, some of…
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Discrete harmonic function in Z^n
There is some gap, in fact I can improve half of the argument of Discrete harmon…
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Log average sarnak conjecture
This is a note concentrate on the log average Sarnak conjecture, after th…
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Two stupid question
The story of the infinite dimensional space of $\Delta$ is following, we elimina…