Presentation

Fully explicit results in multiplicative number theory are often scattered through the litterature. The aim of this site is to present annoted bibliographies in order to keep track of the current knowledge. By the way, the acronym TME-EMT stands for
Théorie Multiplicative Explicite des nombres  /  Explicit Multiplicative number Theory
Here are the contributors for now: Olivier Bordellès, Pierre Dusart, Charles Greathouse, Harald Helfgott, Pieter Moree, Akhilesh P, Olivier Ramaré, Enrique Treviño.

[22 Septembre 2021]    Working on it !  [September 22nd, 2021]

• Averages of arithmetical functions
• Exact computations
• General analytical tools
• Exponential sums / points close to curves
• Size of $L(1,\chi)$ and character sums

 Notation is standard, except maybe for the following one: we write $f=\mathcal{O}^*(g)$ to say that $|f|\le g$. This is simply a Landau-bigO symbol with an implied constant equal to one. Furthermore, the letter $p$ always denotes a prime variable.

How to contribute?

Everyone is most welcome to help us keep track of the results. You can do so by simply sending the development team a mail with the proper information (in bibtex format for the relevant part).
You may also propose a new annoted bibliography, for instance for "Explicit results in the combinatorial sieve", or any other missing entry.
There are other ways to contribute, like modifying the CSS so that this site would be readable under windows, a fact we do not guarantee. Or by proposing a rewrite of some already present bibliography. Or anything else we did not think about :)

How to write?

This part is technical and aimed at the development team only.
• [A] Sections are coded via <div class="section">1. Title</div>. The numbering is done by hand.
• [B] Theorems, Lemmas, Propositions are coded via

<br><span class="THM">Theorem (1986)</span>
<blockquote class="outer-thm">
<div class="thm"> Every zero $\rho$ of $\zeta$ that have a real part between 0 and 1 and an imaginary part not more, in absolute value, than $\le T_0=545\,439\,823$ are in fact on the critical line, i.e. satisfy $\Re \rho=1/2$. </div></blockquote>
• [C] Mathematics are entered latex style and processed via MathJax. Macros are to be avoided, of course.
• [D] A reference is introduced on one line in the form <script language="javascript">bibref("Ramare*12")</script> where Ramare*12 is the key of the bibtex entry, which has to be introduced in the Local-TME-EMT.bib file :)