All Questions

I am considering a PhD research topic. I only have a math Bachelor's degree with working experience mostly in teaching and I have been working on a paper. I have deep interest in Fourier Series and ...

I have a research-level but not necessarily new question about certain equidistribution problems. If $\phi \in L^2(S^2)$ then we could define the Weyl sums: $$ \int \phi \, \mu_d = \frac{1}{|\mathcal{...

For $S\subset \mathbb{N}$ define the upper density as $D^{\ast }(S)=\limsup_{n\rightarrow \infty }\frac{\left\vert S\cap \{1,2,\ldots,n\} \right\vert }{% \left\vert n\right\vert }.$ Question: ...

Let $G := \langle a, b, c \rangle < {\rm Sym}(\mathbb{Z}^2)$ be the group generated by the permutation $$ a: \ (m,n) \ \mapsto \ (m-n,m) $$ of order $6$ and the involutions $$ b: \ (m,n) \ \...

I've been exploring the composition of essentially the Dedekind $\eta$-function with parabolic Möbius transformations, $$C_L(z,t)=\left(\frac{z}{-tz+1}\right)^{\frac{1}{2}}\eta\left(\frac{z}{-tz+1}\...

I've been reading some wonderful blog entries where Terry Tao and Ben Green prove some generalizations of Weyl Equidstribution using a "higher" Fourier Analysis. Unfortunately, all the information I ...