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Linear metric on F2, free group with two generator.
I may have made a stupid mistake, but if not, we could construct a metric by pul…
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Almost orthogonality
Motivation and Cotlar’s lemma We always need to consider a transform $lat…
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The correlation of Mobius function and nil-sequences in short interval
I wish to establish the following estimate: Conjecture :(correlation of Mobius f…
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An Fourier coefficient decay estimate.
f is a matrix value analytic function on $latex \mathbb T$, we know $latex h(f)&…
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Geometric intuition of mean value property of nonlinear elliptic equation
I wish to gain some understanding of the MVP of nonlinear elliptic equation by g…
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Diophantine approximation of algebraic number
An important theorem in Diophantine approximation is the theorem of Liuoville: *…
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Rotation number
Consider compact 1 dimension dynamic system. We focus on $latex S_1$, it …
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Eloquent theory
Consider matrix ODE: $latex \dot{\phi}(t)=A(t)\phi(t)$ Where $latex A(t)$ is a g…
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Van der curpurt trick
There is the statement of Van der carport theorem: Given a sequences $ \{x_n\}_{…
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Multiplication function on short interval
The most important beakgrouth of analytic number theory is the new understanding…