Sylvain JULIEN
  • Member for 10 years, 10 months
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Proposals for polymath projects
15 votes

Hoping it is not too famous an open problem, I would suggest trying to (dis)prove that Euler's constant $\gamma$, defined as $\displaystyle{\lim_{n\to\infty}H_{n}-\log n}$ where $H_{n}$ is the $n$-th ...

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Have there been any updates on Mochizuki's proposed proof of the abc conjecture?
14 votes

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

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Research-only permanent positions worldwide
14 votes

In France again, IHES (Institut des Hautes Etudes Scientifiques), maybe a kind of Princeton's IAS "à la française".

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Most important mathematical results in last 30 years
11 votes

Taniyama, Shimura and later Weil conjectured around 60 years ago that the L-function of an elliptic curve arises from a modular form. This conjecture was known to entail the last Fermat theorem after ...

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What are some important but still unsolved problems in mathematical logic?
9 votes

Woodin's omega conjecture. See this pdf

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Examples of conjectures that were widely believed to be true but later proved false
7 votes

Fermat's conjecture that all numbers of the form $ F_{n} : =2^{2^{n}}+1 $ are prime. Euler proved that $ 641\mid F_{5} $ .

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How can an extremely mathematically talented young person be helped to fulfill his/her potential?
7 votes

What matters here is not how to help him/her to fulfill his/her potential, but how to help him/her be happy in life. Being different is not easy to deal with, and often leads to loneliness or social ...

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Remarkable articles about the distribution of prime numbers that were written by contemporary physicists
6 votes

Marek Wolf, a Polish physicist, is the author of several articles about the distribution of prime numbers. He studied jumping champions and provided a heuristic formula refining Cramer's conjecture, ...

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Constant $a$ such that $[a^n]$ is always prime for $n\in N^+$
6 votes

Maybe not exactly what you're looking for, but in his book "Merveilleux nombres premiers" (in French), Jean-Paul Delahaye mentions the so-called Mills' constant $A=1.30637788386...$ which fulfills, ...

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Math French Words
6 votes

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 ...

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Consequences of Goldbach's Conjecture
5 votes

Only a partial answer as it is too long for a mere comment. There are known connections between non vanishing of L-functions and some versions of the Goldbach conjecture. Gautami Bhowmik showed that ...

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General principles which lead to good questions in many concrete situations
5 votes

A good principle would be to apply this piece of advice from Hermann Weyl : to understand well a mathematical object, determine and study the structure of its group of automorphisms.

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Implicit constant in Tenenbaum's result
Accepted answer
5 votes

In the French edition, it is said that the considered constant does not exceed $4(1+9\lambda_{1}+\lambda_{1}\lambda_{2}/(2-\lambda_{2})^2)$ where $\lambda_{1}>0$, $0\leq \lambda_{2}<2$ are such ...

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References for general Hasse-Weil zeta function
4 votes

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.

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$\log(x)$ or $\ln(x)$ to denote the natural logarithm in research papers?
Accepted answer
4 votes

In number theory, the notation $ \log $ is commonly used, especially when asymptotics are considered. One also frequently uses the notation $ \log_{k} $ for the $ k $ -th iterate of this function. ...

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Has this Peculiar Property of Unit Circles Already been Noticed?
4 votes

This is related to the fact that the circle has constant curvature. Indeed the curvature of a curve obtained plotting $ y=f(x) $ is $\mathcal{C}_{f}(x)=f''(x)(1+(f'(x))^{2})^{-3/2} $, which comes ...

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Mathematical software wish list
4 votes

I'd like to have on a usb key a user friendly software that could parse a math article to check the proofs in it without having to learn how to use stuff like Coq and highlight the possible gaps. But ...

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Your favorite surprising connections in mathematics
4 votes

Definitely not a pure interplay between two subfields of math, but the omnipresence of quaternions in physics is stunning. I even figured out a few years ago that writing down the equivalent of Cauchy-...

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Are the nontrivial zeros of the Riemann zeta simple?
4 votes

I finally managed to find back the article I was talking about. Just click on the green link in the first message of the following link: link text

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Each mathematician has only a few tricks
3 votes

Characterizing a class of integers sharing some property $P$ by defining an arithmetic function taking a single value $k_{P}$ at those integers and then give an equivalent of this arithmetic function. ...

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Harmonic sums and elementary number theory
3 votes

Any $n$ which is of the form $4P$ where $P$ is a perfect number is good: just consider as a set $\{a_{i}\}$ the set of its divisors. As the sum of the reciprocals thereof equals $2$, this guarantees ...

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A book you would like to write
3 votes

I'm not really sure this is a suitable answer to your question, but I'd like to have my recently published novel "Sahelios", in which a Japanese highschool student named Satori (Japanese female given ...

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Is $\Bigl\{ n \sum_{k=2}^{n-1} \frac{1}{k}\Bigr\}$ unique $\forall n \in \Bbb{N}, n>1$
2 votes

Only a partial answer for now, as it is too long for a comment. From my comment and Carlo Beenakker's answer, it suffices to consider the case where $n$ and $m$ have different radicals but the same ...

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Convergence of Euler product and Dirichlet series in the same half-plane?
2 votes

Maybe not exactly what you're looking for, but you may be interested in this preprint by Kaczorowski and Perelli: arXiv:1506.07630 where the authors study the links between several kinds of ...

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What can this $\int_{0}^{t} (\pi(x)-Li(x)) dx$ tell us about primes distribution?
Accepted answer
2 votes

The integral does not converge. See https://academic.oup.com/blms/article-abstract/31/4/424/277640?redirectedFrom=fulltext. On the other hand, a proof that this integral is less than $K.t^{\alpha}$ ...

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On the real part of the Riemann zeta function inside the critical strip
2 votes

See https://www.researchgate.net/publication/321187136_Pair_Correlation_of_Zeros_of_the_Real_and_Imaginary_Parts_of_the_Riemann_Zeta-Function where the authors investigate the behavior of the real ...

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Source for analysis of identification of structures in learner's mind and mathematical structures?
2 votes

Grothendieck wrote a text entitled "Structure de la psyché" that might help shed a light on the issues you consider. As a former member of Bourbaki, it seems highly plausible that he tried doing so to ...

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Learning German and Russian for reading old mathematical papers in these languages
2 votes

The French publisher Assimil is very good (and famous) to get conversational skills in many foreign languages. As for the mathematical words, you can use Wikipedia, that's how I got to know that the ...

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Can Voronin's universality theorem be used to show that $\sigma\circ\zeta=\zeta\circ\sigma$ implies $\sigma$ continuous?
2 votes

I apologize for answering my own question, but it has turned out that the statement I consider can actually be proved without using Voronin's theorem. Here comes an excerpt from an article of mine ...

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Fantastic properties of Z/2Z
2 votes

RH holds if and only if the group of isometries of the complex plane that preserve globally the multiset of non-trivial zeroes of the Riemann Zeta function is isomorphic to $Z/2Z$ (otherwise, it would ...

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