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location France
age 32
visits member for 3 years, 4 months
seen 4 hours ago

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/about-goldbachs-conjecture). 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 Hardy-Littlewood k-tuple 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 L-functions
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 Rankin-Selberg 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 "Rankin-Selberg" L-functions in it.
Jun
7
comment absolute convergence of Rankin-Selberg series
A bit off-topic, 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 Polya-like Fourier transforms?
If i'm not mistaken, the so-called De Bruijn-Newman 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 $\Lambda>-2.7E-9$.
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 $\lim\inf_{n\to\infty}p_{n+k}-p_{n}=O(k\log k)$?
added 823 characters in body
Jun
1
revised Would the following conjectures imply $\lim\inf_{n\to\infty}p_{n+k}-p_{n}=O(k\log k)$?
added 823 characters in body