# Wave Divisor Function

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#### OOOVincentOOO

Error Divisor Summatory Function

Hello,

Did allot of calculations last days. Did not see any patterns and wanted to throw all in bin.

I think I found a way to numerical determine error in Divisor Summatory function (Dirichlet).

$\Theta(x \rightarrow 0) \approx 0.5$

$\Theta_{min}(x \approx 11) \approx 0.26$

For calculations see Jupyter notebook:

https://mybinder.org/v2/gh/oooVincentooo/Shared/master?filepath=Wave%20Divisor%20Function%20rev%202.4.ipynb

My holiday's is almost over, last weekend. Hoped that someone could verify or look into results.

Best regards,

Vincent Preemen

#### OOOVincentOOO

Results are wrong made some mistakes.

Was just luck achieving these results.

Do understand even less.

Need more time to think. Time out for now!

#### OOOVincentOOO

Wave Divisor Function Arcsine Distribution

Hello,

Determining $$\displaystyle \Theta$$ from divisor summatory requires more thinking of me. There are many solutions for the divisor function. My simple "math" skills reaches it's limit.

In the meantime I studied on some of the properties of the arcsine distribution. To my understanding for $\infty$ the error is arcsine distributed.

There are some interesting properties. Demonstrated in the Jupyter notebook two cases of the acrsine distribution:

- Without resonation and with resonation.

As screenshot:

Jupyter Notebook (Arcsine):
https://mybinder.org/v2/gh/oooVincentooo/Shared/master?filepath=Wave%20Divisor%20Function%20Arcsine.ipynb

Hope that someone has some input or advice.

Jupyter notebooks should open online (in cloud) and are interactive after loading Menu: [Cell]+>[Run All]. Does not work with IE, other browser do. First loading might take some time.

Best regards,

Vincent

Note:
I also updated main notebook file. Fixed some typo's and improved description of the error:
https://mybinder.org/v2/gh/oooVincentooo/Shared/master?filepath=Wave%20Divisor%20Function%20rev%202.4.ipynb

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#### greg1313

Forum Staff
This isn't a blogging site.

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