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38 votes
2 answers
13k views

What, exactly, has Louis de Branges proved about the Riemann Hypothesis?

I know this is a dangerous topic which could attract many cranks and nutters, but: According to Wikipedia [and probably his own website, but I have a hard time seeing exactly what he's claiming] Louis ...
Zen Harper's user avatar
  • 1,990
3 votes
0 answers
646 views

On properties on a certain functional

Consider the following function: $$F(z) = \omega(z)\sin^2\left(\frac{c\Gamma(z)}{z}\right)$$ Here, $\omega(z)$ is a weight we have to construct and $c$ is a constant. The following three conditions ...
bambi's user avatar
  • 375
5 votes
2 answers
418 views

A question about Schwartz-type functions used in analytic number theory

In analytic number theory we like to weigh our counting functions with a smooth function $f$, so that we may apply Poisson's summation formula and take advantage of Fourier transforms. Typically the ...
Stanley Yao Xiao's user avatar
2 votes
0 answers
95 views

Uncertainty principle: minimize $\int_{-\infty}^\infty |t| |\widehat{f}(t)|^2 dt$ for $f$ of compact support

This is a question of uncertainty-principle type stemming from Eigenvalue of a convolution and a restriction? Let $f:\mathbb{R}\to \mathbb{R}$ be even, absolutely continuous and supported in $[-\frac{...
H A Helfgott's user avatar
  • 20.2k
0 votes
0 answers
171 views

Explanation of a step in a preprinted work

I have been studying this preprinted paper and the references therein. I believe that there are some typos; However, since I am not an expert yet, I would like to make sure I am correct. I do not ...
Mr. Proof's user avatar
  • 159
-2 votes
1 answer
314 views

Series representation for $\log(|\zeta(\frac{1}{2}+it)|)$

(Question is short and straight-forward. ) What is/are "nice and non-trivial" series representation/s of $\log(|\zeta(\frac{1}{2}+it)|)$ ?? By "nice and non-trivial" I mean contains no ...
bambi's user avatar
  • 375