arXiv subjects

M'hammed Ziane

Publications and source records attributed to M'hammed Ziane.

2 recordsLinked to original sources

arXiv2018

A note on the extended Bruinier-Kohnen conjecture

Let $f$ be a cuspform of integral half-weight $k+1/2$, whose Fourier coefficients $a(n)$ not necessarily real. We verify partially an extension of a conjecture of Bruinier and Kohnen on the equi-distribution of the signs of $a(n)$ (when are real), conjectured by the first author in \cite{Amri2} for the sequence $\{a(tp^{2ν})\}_{p,\text{prime}}$, where $ν$ an odd positive integer and $t$ a square-free integer.

math.NT↗

arXiv2018

p-Rational Fields and the Structure of Some Modules

Assume that the field $K$ is $p$-rational. We study the freeness of the $Λ(G_{\infty,S})$-module $\mathcal{X}=\mathcal{H}^{ab}=\mathrm{\mathrm{G}al}(K_{S\cup S_p}/K_{\infty,S})^{ab}$. For numerical evidence to our result we consider the case of fields of the form $\mathbb{Q}(\sqrt{pq},\sqrt{-d})$.

math.NT↗