#zetafunction — Public Fediverse posts
Live and recent posts from across the Fediverse tagged #zetafunction, aggregated by home.social.
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“If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?” – David Hilbert
#RiemannHypothesis #DavidHilbert #RiemannZetaFunction #ZetaFunction #UnsolvedProblem #MathHistory #Hilbert #Riemann
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“If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?” – David Hilbert
#RiemannHypothesis #DavidHilbert #RiemannZetaFunction #ZetaFunction #UnsolvedProblem #MathHistory #Hilbert #Riemann
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“If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proven?” – David Hilbert
#RiemannHypothesis #DavidHilbert #RiemannZetaFunction #ZetaFunction #UnsolvedProblem #MathHistory #Hilbert #Riemann
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The Riemann Hypothesis: Past, Present and a Letter Through Time
https://arxiv.org/abs/2602.04022#RiemannHypothesis #Riemann #Conjecture #Hypothesis #ZetaFunction #RiemanZetaFunction #RH #MillenniumPrizeProblems #PrimeNumbers
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The Riemann Hypothesis: Past, Present and a Letter Through Time
https://arxiv.org/abs/2602.04022#RiemannHypothesis #Riemann #Conjecture #Hypothesis #ZetaFunction #RiemanZetaFunction #RH #MillenniumPrizeProblems #PrimeNumbers
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The Riemann Hypothesis: Past, Present and a Letter Through Time
https://arxiv.org/abs/2602.04022#RiemannHypothesis #Riemann #Conjecture #Hypothesis #ZetaFunction #RiemanZetaFunction #RH #MillenniumPrizeProblems #PrimeNumbers
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📢 NEW WORK: "Origin of the constant B ≈ 0.486 in the distribution of prime numbers"
I study the Gaussian decay of a prime-related sum: S(s) ~ e^{-Bs²}. The constant B ≈ 0.486 emerges from three perspectives:
🔹 Arithmetic: B ≈ Σ 1/π(eⁿ) − 1
🔹 Spectral (under RH): B linked to zeros of ζ(s)
🔹 Geometric: the base e is optimal📄 Full paper: [PDF_LINK]
👤 My other work: [ACADEMIA_LINK]Open question: Which approach seems most enlightening to you?
#NumberTheory #PrimeNumbers #ZetaFunction #Maths #Mathematics #Research #RiemannHypothesis #Preprint #PrimeDistributionrime_numbers
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📢 NEW WORK: "Origin of the constant B ≈ 0.486 in the distribution of prime numbers"
I study the Gaussian decay of a prime-related sum: S(s) ~ e^{-Bs²}. The constant B ≈ 0.486 emerges from three perspectives:
🔹 Arithmetic: B ≈ Σ 1/π(eⁿ) − 1
🔹 Spectral (under RH): B linked to zeros of ζ(s)
🔹 Geometric: the base e is optimal📄 Full paper: [PDF_LINK]
👤 My other work: [ACADEMIA_LINK]Open question: Which approach seems most enlightening to you?
#NumberTheory #PrimeNumbers #ZetaFunction #Maths #Mathematics #Research #RiemannHypothesis #Preprint #PrimeDistributionrime_numbers
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📢 NEW WORK: "Origin of the constant B ≈ 0.486 in the distribution of prime numbers"
I study the Gaussian decay of a prime-related sum: S(s) ~ e^{-Bs²}. The constant B ≈ 0.486 emerges from three perspectives:
🔹 Arithmetic: B ≈ Σ 1/π(eⁿ) − 1
🔹 Spectral (under RH): B linked to zeros of ζ(s)
🔹 Geometric: the base e is optimal📄 Full paper: [PDF_LINK]
👤 My other work: [ACADEMIA_LINK]Open question: Which approach seems most enlightening to you?
#NumberTheory #PrimeNumbers #ZetaFunction #Maths #Mathematics #Research #RiemannHypothesis #Preprint #PrimeDistributionrime_numbers
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📢 NEW WORK: "Origin of the constant B ≈ 0.486 in the distribution of prime numbers"
I study the Gaussian decay of a prime-related sum: S(s) ~ e^{-Bs²}. The constant B ≈ 0.486 emerges from three perspectives:
🔹 Arithmetic: B ≈ Σ 1/π(eⁿ) − 1
🔹 Spectral (under RH): B linked to zeros of ζ(s)
🔹 Geometric: the base e is optimal📄 Full paper: [PDF_LINK]
👤 My other work: [ACADEMIA_LINK]Open question: Which approach seems most enlightening to you?
#NumberTheory #PrimeNumbers #ZetaFunction #Maths #Mathematics #Research #RiemannHypothesis #Preprint #PrimeDistributionrime_numbers
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📢 NEW WORK: "Origin of the constant B ≈ 0.486 in the distribution of prime numbers"
I study the Gaussian decay of a prime-related sum: S(s) ~ e^{-Bs²}. The constant B ≈ 0.486 emerges from three perspectives:
🔹 Arithmetic: B ≈ Σ 1/π(eⁿ) − 1
🔹 Spectral (under RH): B linked to zeros of ζ(s)
🔹 Geometric: the base e is optimal📄 Full paper: [PDF_LINK]
👤 My other work: [ACADEMIA_LINK]Open question: Which approach seems most enlightening to you?
#NumberTheory #PrimeNumbers #ZetaFunction #Maths #Mathematics #Research #RiemannHypothesis #Preprint #PrimeDistributionrime_numbers
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🚀 New preprint out on Cambridge Open Engage:
“A Fully Invertible Global Analytic Model of the Riemann Zeta Function”I introduce Sui Theory to construct a globally analytic and invertible framework for ζ(s) in Hardy space H²(ℂ⁺).
🔗 Cambridge Open Engage - https://bit.ly/461M67F
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🚀 New preprint out on Cambridge Open Engage:
“A Fully Invertible Global Analytic Model of the Riemann Zeta Function”I introduce Sui Theory to construct a globally analytic and invertible framework for ζ(s) in Hardy space H²(ℂ⁺).
🔗 Cambridge Open Engage - https://bit.ly/461M67F
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🚀 New preprint out on Cambridge Open Engage:
“A Fully Invertible Global Analytic Model of the Riemann Zeta Function”I introduce Sui Theory to construct a globally analytic and invertible framework for ζ(s) in Hardy space H²(ℂ⁺).
🔗 Cambridge Open Engage - https://bit.ly/461M67F
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🚀 New preprint out on Cambridge Open Engage:
“A Fully Invertible Global Analytic Model of the Riemann Zeta Function”I introduce Sui Theory to construct a globally analytic and invertible framework for ζ(s) in Hardy space H²(ℂ⁺).
🔗 Cambridge Open Engage - https://bit.ly/461M67F
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One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅
#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals
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One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅
#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals
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One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅
#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals
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One of the best things I saw this week: a paper uncovering alien signals in the Riemann Zeta function. April Fools always brings peak creativity. 😅
#Riemann #Zeta #ZetaFunction #RiemanZetaFunction #AprilFool #AprilFools #AprilFoolsDay #Creativity #Math #Maths #NumberTheory #PeakCreativity #Nerd #Nerds #Humor #Humour #Alien #AlienSignals
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Decades-Long Quest for the Irrational: A Breakthrough in Number Theory
In a stunning revelation, mathematicians have expanded upon Roger Apéry's groundbreaking proof of the irrationality of ζ(3), paving the way for a new era in number theory. This innovative approach not...
https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory
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Decades-Long Quest for the Irrational: A Breakthrough in Number Theory
In a stunning revelation, mathematicians have expanded upon Roger Apéry's groundbreaking proof of the irrationality of ζ(3), paving the way for a new era in number theory. This innovative approach not...
https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory
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Decades-Long Quest for the Irrational: A Breakthrough in Number Theory
In a stunning revelation, mathematicians have expanded upon Roger Apéry's groundbreaking proof of the irrationality of ζ(3), paving the way for a new era in number theory. This innovative approach not...
https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory
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Decades-Long Quest for the Irrational: A Breakthrough in Number Theory
In a stunning revelation, mathematicians have expanded upon Roger Apéry's groundbreaking proof of the irrationality of ζ(3), paving the way for a new era in number theory. This innovative approach not...
https://news.lavx.hu/article/decades-long-quest-for-the-irrational-a-breakthrough-in-number-theory
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@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
https://www.youtube.com/watch?v=YuIIjLr6vUA
#maths #AnalyticContinuation #Ramanujan -
@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
https://www.youtube.com/watch?v=YuIIjLr6vUA
#maths #AnalyticContinuation #Ramanujan -
@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
https://www.youtube.com/watch?v=YuIIjLr6vUA
#maths #AnalyticContinuation #Ramanujan -
@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
https://www.youtube.com/watch?v=YuIIjLr6vUA
#maths #AnalyticContinuation #Ramanujan -
Interesting integral! #Challenge
\[\displaystyle\int_0^1\dfrac{\ln (x)\ln(1-x)}{x(1-x)}\operatorname{Li}_2(x)\ dx=5\zeta(2)\zeta(3)-8\zeta(5)\]
Where \(\operatorname{Li}_2(x)\) denotes the dilogarithm (or Spence's function), and \(\zeta(x)\) denotes the Riemann zeta function.#ZetaFunction #Zeta #Dilogarithm #SpenceFunction #Polylogarithm #Integral #DefiniteIntegral #Integration #Integrals #RiemannZetaFunction #Logarithm #Function #LogarithmicFunction
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Interesting integral! #Challenge
\[\displaystyle\int_0^1\dfrac{\ln (x)\ln(1-x)}{x(1-x)}\operatorname{Li}_2(x)\ dx=5\zeta(2)\zeta(3)-8\zeta(5)\]
Where \(\operatorname{Li}_2(x)\) denotes the dilogarithm (or Spence's function), and \(\zeta(x)\) denotes the Riemann zeta function.#ZetaFunction #Zeta #Dilogarithm #SpenceFunction #Polylogarithm #Integral #DefiniteIntegral #Integration #Integrals #RiemannZetaFunction #Logarithm #Function #LogarithmicFunction
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A representation of \(18\) using an analytic continuation of the Dirichlet series and the numbers \(0, 1,2,3,4,5,6\).
\[18=\left|\dfrac{1}{\zeta^2(0)}\left(\dfrac{\mathcal{H}(-6)}{\zeta(-5)}-\dfrac{\mathcal{H}(-2)}{\zeta(-1)}\right)\dfrac{\mathcal{H}(-4)}{\zeta(-3)}\right|\]
where \(\displaystyle\zeta(z)=\sum_{n\geq1}\dfrac{1}{n^z}\) denotes the Riemann zeta function, and \(\displaystyle\mathcal{H}(z)=\sum_{n\geq1}\dfrac{H_n}{n^z}\) denotes the harmonic zeta function.#ZetaFunction #RiemannZetaFunction #HarmonicZetaFunction #AnalyticContinuation #DirichletSeries #Series #Numbers #Zeta #Harmonic #HarmonicNumbers #Representation #Function #Expression
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There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction -
There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction -
There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction -
There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction -
There is this really awesome series on YouTube about the Riemann-Zeta function which is currently running and seems to want to explain all the mathematic objects related to it properly it would be awesome if you could show the video series some love while it's running. https://youtu.be/4bzSFNCiKrk
#mathematics #mathstodon #primenumbers #riemann #zetafunction -
PRODUCTS OVER PRIME NUMBERS [2/2]:
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p+1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-3}}{1-p^{-2}}=\dfrac{\zeta(2)}{\zeta(3)}=\dfrac{\pi^2}{6\zeta(3)}\]
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p-1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-6}}{(1-p^{-2})(1-p^{-3})}=\dfrac{\zeta(2)\zeta(3)}{\zeta(6)}=\dfrac{315}{2\pi^4}\zeta(3)\]
#PrimeProducts #RiemannZetaFunction #EulerProduct #ZetaFunction #InfiniteProduct #NumberTheory -
PRODUCTS OVER PRIME NUMBERS [2/2]:
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p+1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-3}}{1-p^{-2}}=\dfrac{\zeta(2)}{\zeta(3)}=\dfrac{\pi^2}{6\zeta(3)}\]
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p-1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-6}}{(1-p^{-2})(1-p^{-3})}=\dfrac{\zeta(2)\zeta(3)}{\zeta(6)}=\dfrac{315}{2\pi^4}\zeta(3)\]
#PrimeProducts #RiemannZetaFunction #EulerProduct #ZetaFunction #InfiniteProduct #NumberTheory -
PRODUCTS OVER PRIME NUMBERS [2/2]:
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p+1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-3}}{1-p^{-2}}=\dfrac{\zeta(2)}{\zeta(3)}=\dfrac{\pi^2}{6\zeta(3)}\]
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p-1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-6}}{(1-p^{-2})(1-p^{-3})}=\dfrac{\zeta(2)\zeta(3)}{\zeta(6)}=\dfrac{315}{2\pi^4}\zeta(3)\]
#PrimeProducts #RiemannZetaFunction #EulerProduct #ZetaFunction #InfiniteProduct #NumberTheory -
PRODUCTS OVER PRIME NUMBERS [2/2]:
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p+1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-3}}{1-p^{-2}}=\dfrac{\zeta(2)}{\zeta(3)}=\dfrac{\pi^2}{6\zeta(3)}\]
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p-1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-6}}{(1-p^{-2})(1-p^{-3})}=\dfrac{\zeta(2)\zeta(3)}{\zeta(6)}=\dfrac{315}{2\pi^4}\zeta(3)\]
#PrimeProducts #RiemannZetaFunction #EulerProduct #ZetaFunction #InfiniteProduct #NumberTheory -
PRODUCTS OVER PRIME NUMBERS [2/2]:
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p+1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-3}}{1-p^{-2}}=\dfrac{\zeta(2)}{\zeta(3)}=\dfrac{\pi^2}{6\zeta(3)}\]
\[\displaystyle\prod_{p\in\mathbb{P}}\left(1+\dfrac{1}{p(p-1)}\right)=\prod_{p\in\mathbb{P}}\dfrac{1-p^{-6}}{(1-p^{-2})(1-p^{-3})}=\dfrac{\zeta(2)\zeta(3)}{\zeta(6)}=\dfrac{315}{2\pi^4}\zeta(3)\]
#PrimeProducts #RiemannZetaFunction #EulerProduct #ZetaFunction #InfiniteProduct #NumberTheory -
Me looking at a formula of :ramanujan: Ramanujan: Yeah, just do partial fractions of the infinite sum, telescope two of the terms, and look at the remaining value of the #ZetaFunction.
Me counting stitches on my #knitting for DPNs: 48 divided by 3 is 18, right?