Content deleted Content added
m Maintain {{WPBS}}: 1 WikiProject template. Remove 1 deprecated parameter: field. Tag: |
|||
| (6 intermediate revisions by 6 users not shown) | |||
Line 1:
{{WikiProject banner shell|class=Start|
{{WikiProject Mathematics| importance=low}}
}}
=== Error? ===
"...Riemann found an explicit formula for the number of primes π(x) less than a given number x."
Should this
I tried to verify mathematically that the formula gives this, but I am not adept enough to work with it much...I did find that the f(x) formula can work either way (if pi(x) includes x, then f(x) includes x; and if pi(x) excludes x, then f(x) excludes x). This was quite simple using induction.
Line 32 ⟶ 30:
Could someone who is familiar with the topic of this page move it to a more specific title? Thanks. [[User:Duoduoduo|Duoduoduo]] ([[User talk:Duoduoduo|talk]]) 13:18, 30 July 2013 (UTC) I would note that the article was originally called "Explicit formulae (L-function)", which sounds perfect to me, but it was moved to "Explicit formula" on 23:32, 8 January 2009 with the edit summary "shorter title". [[User:Duoduoduo|Duoduoduo]] ([[User talk:Duoduoduo|talk]]) 13:39, 30 July 2013 (UTC)
should it be renamed as 'explicit formulae relating prime numbers and riemann zeros ' ? since it's a relationship between prime numbers and Riemann zeros <!-- Template:Unsigned IP --><small class="autosigned">— Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[Special:Contributions/82.130.159.27|82.130.159.27]] ([[User talk:82.130.159.27#top|talk]]) 12:18, 23 February 2017 (UTC)</small> <!--Autosigned by SineBot-->
== Weil's Explicit Formula ==
Some of the formulas under this topic don't look correct to me.
'''Question (1)''': In the formula <math>\frac{d}{du} \left[ \sum\limits_{n \le e^{|u|}} \Lambda(n) + \frac{1}{2} \ln(1-e^{-2|u|})\right] </math><math>= \sum\limits_{n=1}^\infty \Lambda(n) \left[ \delta(u-\ln n) + \delta(u-\ln n) \right] + \frac{d\ln(1-e^{-2|u|})}{du} = e^u - \sum{\rho} e^{\rho u} </math>,
'''(1a)''' Should <math>\left[ \delta(u-\ln n) + \delta(u-\ln n) \right]</math> be <math>\left(\delta(u-\ln n)+\delta(u+\ln n)\right)</math>?
'''(1b)''' Should <math>\frac{d\ln(1-e^{-2|u|})}{du}</math> be <math>\frac{1}{2}\frac{d\ln(1-e^{-2|u|})}{du}</math>?
'''(1c)''' Should <math>\sum{\rho} e^{\rho u} </math> be <math>\sum\limits_{\rho}{\rho}\,e^{\rho u}</math> or <math>\sum\limits_{\rho}\,e^{\rho u}</math>?
'''Question (2)''': In the last paragraph should <math>g(u) = \sum_{n=1}^\infty \Lambda(n) \left[ \delta(u-\ln n) + \delta(u-\ln n) \right] </math> be <math>g(u)=\sum_{n=1}^\infty\Lambda(n)\left(\delta(u-\ln n)+\delta(u+\ln n)\right)</math>?
[[User:StvC|StvC]] ([[User talk:StvC|talk]]) 22:30, 28 February 2019 (UTC)
| |||