bio | website | |
---|---|---|
location | France | |
age | 32 | |
visits | member for | 3 years, 5 months |
seen | 11 hours ago | |
stats | profile views | 2,772 |
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.
Aug 27 |
comment |
Primality matrices
I've been told by a brilliant youngster that the upper bound $\alpha_{n}\ll n^{1/2+\varepsilon}$ implies GRH (that is, RH for Dirichlet L-functions). I have no idea how to prove that such an upper bound is a consequence of RH though. I'll try to figure it out this weekend. |
Aug 26 |
revised |
Primality matrices
added 3261 characters in body |
Aug 25 |
comment |
Primality matrices
What is unclear precisely? Should I paste the content of the link to help people understand what a potential typical primality radius is? |
Aug 24 |
revised |
Primality matrices
added 97 characters in body |
Aug 24 |
revised |
Primality matrices
added 103 characters in body |
Aug 23 |
asked | Primality matrices |
Aug 6 |
revised |
About Goldbach's conjecture
added 207 characters in body |
Aug 5 |
accepted | Best error terms for functions related to square free numbers |
Aug 5 |
comment |
The shortest interval for which the prime number theorem holds
My Robert&Collins dictionary confirms that the noun needs an 's'. It's the first time (and probably the last too) that I'm right against Terence Tao, but unfortunately not in number theory... |
Aug 5 |
comment |
The shortest interval for which the prime number theorem holds
Aside any mathematical consideration, and even though English is not my mother tongue, it seems that 'heuristic' is an adjective whereas the corresponding noun is 'heuristics' with an 's' as in 'physics'. Apart from that this question appears to be very interesting and I would be thrilled to learn that the considered heuristics would finally turn out to be correct. |
Aug 5 |
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The shortest interval for which the prime number theorem holds
Simply a given non trivial zero of a given primitive L-function F should be analogous to an algebraic number determining its minimal polynomial and its different conjugates, which would be the other non trivial zeros of F in this analogy. |
Aug 5 |
asked | Best error terms for functions related to square free numbers |
Aug 5 |
comment |
The shortest interval for which the prime number theorem holds
I know, but Haseo Ki et al. suggest in an article about the unicity of l-functions in the extended Selberg class that it is likely that no two such L-functions share a non trivial zero. This would mean that a single non trivial zero determines entirely an l-function, and thus its non trivial zeros may depend on one another in some way. Moreover I shall give an argument in favor of the conjecture above when I'm back home. |
Aug 5 |
comment |
The shortest interval for which the prime number theorem holds
Is there any link with the conjecture $M(x)\ll\sqrt{x}$ with $M(x)$ the summatory function of the Möbius function? |
Aug 5 |
accepted | is there any heuristics suggesting that the number of Fibonacci primes below $x$ is equivalent to $\log_{\phi}\log_{\phi}x$? |
Aug 4 |
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Does $\pi(n+r)+\pi(n-r)$ decrease as $r$ increases?
@Jeremy Rickard: thank you for the counterexample. Still, it would be rather interesting to know the frequency of such "anomalous" variations of the considered quantity. |
Aug 4 |
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is there any heuristics suggesting that the number of Fibonacci primes below $x$ is equivalent to $\log_{\phi}\log_{\phi}x$?
A Fibonacci prime is a prime occurring in Fibonacci sequence, and $\phi=\dfrac{1+\sqrt{5}}{2}$ is the so-called golden ratio. |
Aug 4 |
asked | Does $\pi(n+r)+\pi(n-r)$ decrease as $r$ increases? |
Aug 4 |
asked | is there any heuristics suggesting that the number of Fibonacci primes below $x$ is equivalent to $\log_{\phi}\log_{\phi}x$? |
Jul 23 |
awarded | Yearling |