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Please notice a few differences between French and English. "Un nombre positif" is a non negative number, "supérieur à" is "greater than or equal to". In English 0 is not a natural number, while in Fr …

Grothendieck, who passed away on November 13, 2014, left a huge amount (around 20.000 sheets) of personal notes in the University of Montpellier that he thought he was the only one to be able to decip …

This recent preprint may be of interest for you, as the authors first consider L-functions and then find back the algebraic variety they come from.

This question might not be suitable for MO since i know nothing about Calabi-yau varieties aside the fact that they are used in string theory to compactify additional dimensions, but still, it makes w …

Sorry for answering my own question, but it may be useful to some people. It seems, judging by http://arxiv.org/pdf/1301.2225v2.pdf, that the "right" notion of L-function for a Calabi-Yau variety is n …

I just read on Google+ that the paper will be published in 2018 in a Japanese journal whose editor-in-chief is Mochizuki himself. See https://plus.google.com/+johncbaez999/posts/DWtbKSG9BWD

Andrew Booker defined the notion of L-datum that encompasses the Selberg class and allows to obtain simplicity results for the non trivial zeroes of some automorphic L-functions. Thomas Oliver, buildi …

Edited after Will Sawin's comment: Consider the set $\mathcal{M}$ of all automorphic L-functions belonging to the Selberg class. Such a set is closed for the product $.$ and the tensor product $\oti …

I've just read on Wikipedia that the original Taniyama conjecture about L-functions of elliptic curves over an arbitrary number field was still unproven. This made me want to know more about this con …

It seems that Lan Nguyen proved in a preprint on arxiv of 2013 that the Tate-Shafarevich group of a rational elliptic curve is finite. However, I couldn't find any published version thereof. So is it …