English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

There are no square $L^2$-flat sequences of polynomials of the type  $$\frac{1}{\sqrt q}( \epsilon_0 + \epsilon_1z + \epsilon_2z^2 + \cdots +\epsilon_{q-2}z^{q-2} +\epsilon_q z^{q-1}),$$ where for each $j,~~ 0 \leq j\leqq-1,~\epsilon_j = \pm 1$. It follows that Erd\"{o}s's conjectures on Littlewoodpolynomials hold. Consequently, Turyn-Golay's conjecture is true, that is,there are only finitely many Barker sequences. We further get that the spectrumof dynamical systems arising from continuous Morse sequences is singular. Thissettles an old question due to M. Keane. Applying our reasoning to theLiouville function we obtain that the popular Chowla conjecture on the%Bernouillicity normality of the Liouville function implies Riemann hypothesis.

On the Erd\"{o}s flat polynomials problem, Chowla conjecture and Riemann Hypothesis