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#Riemann

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Cheryl Furse

I have no clue, what my AI is talking about. I am not physicist or mathematician but it looks intelligent lol I fed my AI with physics and mathematics textbooks. So it should know what it talks about. But without knowledge about this theme it seems a bit stressing to follow his answers. lol

#ai#gpt4all#mathematics
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Rod2ik 🇪🇺 🇨🇵 🇪🇸 🇺🇦 🇨🇦 🇩🇰 🇬🇱

Une avancée notable vers la résolution de l' #hypothèse de #Riemann .

Poir cela, #LarryGuth et #JamesMaynard utilisent des #polynômes de #Dirichlet et une meilleure borne de leurs zéros.

Référence : arxiv.org/abs/2405.20552

mundodeportivo.com/urbantecno/

arXiv.orgNew large value estimates for Dirichlet polynomialsWe prove new bounds for how often Dirichlet polynomials can take large values. This gives improved estimates for a Dirichlet polynomial of length $N$ taking values of size close to $N^{3/4}$, which is the critical situation for several estimates in analytic number theory connected to prime numbers and the Riemann zeta function. As a consequence, we deduce a zero density estimate $N(σ,T)\le T^{30(1-σ)/13+o(1)}$ and asymptotics for primes in short intervals of length $x^{17/30+o(1)}$.
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ƧƿѦςɛ♏ѦਹѤʞ

@zvavybir
It does diverge. It has no sum.
However, the uniquely valued #Riemann #ZetaFunction can be analytically continued into the left half-plane where we find zeta(-1)=-1/12 (which 'looks like' 1+2+...). #Cesàro #summation will get you part of the way there also, and, as you say, yields the same result; presumably due to some ultimate cosmic logical rightness :-)
I very strongly recommend BP's superb exposition of this issue
youtube.com/watch?v=YuIIjLr6vU
#maths #AnalyticContinuation #Ramanujan

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katch wreck

`Two years later, in 1849, he returned to Göttingen to pursue his PhD with Gauss, completing his thesis in 1851 on the theory of complex variables, the basis for what we now call Riemann surfaces. Gauss described Riemann as having “a gloriously fertile originality” in his report on the thesis, and two years later, when #Riemann was required to give a lecture to land a faculty position at Göttingen, Gauss assigned his star pupil the topic of the foundations of #geometry`

aps.org/archives/publications/

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