bio  website  

location  France  
age  32  
visits  member for  3 years, 4 months 
seen  4 hours ago  
stats  profile views  2,706 
I'm a former student in physics fond of number theory, especially Hilbert's 8th problem, further generalizations of the Riemann Hypothesis and almost everything related to prime numbers and L Functions. I'm also interested in Galois Theory even though I still don't know much about it.
16h

awarded  Yearling 
20h

comment 
Lower bound for a prime gap occurring infinitely often
So could we deduce from the twin prime conjecture that the number of twin primes below $x$ is $\gg x/log^{2} x$? 
20h

accepted  Lower bound for a prime gap occurring infinitely often 
23h

asked  Lower bound for a prime gap occurring infinitely often 
2d

accepted  Asymptotics and error terms for an arithmetic function built upon $\omega$ and $\Omega$ functions 
2d

asked  Asymptotics and error terms for an arithmetic function built upon $\omega$ and $\Omega$ functions 
Jul 15 
comment 
If there are two primes at an even distance $k$ is there another disjoint pair of primes also at distance $k$?
This boils down to showing that any positive integer is a primality radius of at least two integers (see mathoverflow.net/questions/61842/aboutgoldbachsconjecture). I think there is some kind of duality between the number $N_{2}(n)$ of primality radii of n and the number $M_{r}(n)$ of integers $m$ below $n$ having a given positive integer $r$ as a primality radius. More precisely I expect the relation $N_{2}(n)\asymp_{r}M_{r}(n)$ to hold, but it remains highly conjectural. 
Jul 15 
comment 
If there are two primes at an even distance $k$ is there another disjoint pair of primes also at distance $k$?
Your question sounds a bit unclear to me: do you require the two primes to be consecutive? 
Jul 14 
accepted  Is HardyLittlewood ktuple conjecture known to imply Goldbach's conjecture? 
Jul 8 
asked  Proportion of rational elliptic curves of a given rank 
Jun 13 
comment 
Advice for number theory library
Try Olivier Bordellès' Arithmetic tales, Springer. If you read French, Tenenbaum's "Introduction à la théorie analytique et probabiliste des nombres" and Colmez' second edition of "Eléments d'analyse et d'algèbre (et de théorie des nombres)" are worth buying. 
Jun 12 
accepted  Product of automorphic Lfunctions 
Jun 8 
comment 
On the sum of consecutive primes and product of first and last
There are $3$ primes in $[2,5]$, $5$ in $[3,13]$, $9$ in $[5,31]$. Maybe you can find a good prime $(p,p')$ pair such that $\pi(p')\pi(p)$ is any given power of $2$. This would settle your first question. By the way, $5$, $13$ and $31$ are examples of primes $p$ such that $2^{p}1$ is prime. So maybe there's some kind of hidden connexion between your good prime pairs and Mersenne primes (and hence with even perfect numbers). Nice question! 
Jun 7 
comment 
absolute convergence of RankinSelberg series
Ok, thanks. My question originated in the possible proof of the PNT for the Selberg class by Yoshikatsu Yashiro, as I wanted to know if it was sufficient to ensure unique factorization in this class but M. Ram Murty told me that one needed the existence of some kind of "RankinSelberg" Lfunctions in it. 
Jun 7 
comment 
absolute convergence of RankinSelberg series
A bit offtopic, but if I'm not mistaken, I was told that the non vanishing on the $\sigma=1$ line of these L functions was needed to ensure unique factorization. Has it been proved that these L functions don't vanish on the considered line? I can ask this question in a new thread if needed. 
Jun 7 
comment 
Are there any new results on approximating Riemann $\Xi$ function by Polyalike Fourier transforms?
If i'm not mistaken, the socalled De BruijnNewman constant $\Lambda$ is defined in such a way that $4\lambda\geq \Lambda$ implies $\Xi_{\lambda}$ has only real zeros. Judging by an article by Haseo Ki, it seems that $\Lambda$ is conjectured to be both non positive and non negative. A quick glance at Wikipedia shows that it was proved in 2000 that $\Lambda>2.7E9$. 
Jun 1 
accepted  Is SOC known to imply the Grand Riemann Hypothesis? 
Jun 1 
asked  Is SOC known to imply the Grand Riemann Hypothesis? 
Jun 1 
revised 
Would the following conjectures imply $\lim\inf_{n\to\infty}p_{n+k}p_{n}=O(k\log k)$?
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Jun 1 
revised 
Would the following conjectures imply $\lim\inf_{n\to\infty}p_{n+k}p_{n}=O(k\log k)$?
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