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ThomRuley 2020-12-11 16:12

OPN Library website
 
I have a class project coming up for school, and part of that project will be to create a website. After discussing with my advisor, this has become a great opportunity to get my planned odd perfect number bibliography/library up and running.

My overall vision for the website would be a location where anyone working on the odd perfect number conjecture would be able to access previously published materials relating to the conjecture or to closely related topics. The "library" would be the first part of the website. Later on, a discussion forum and one or more DC projects may be added to this web presence.

First, I would like to start with the library section:
As the anticipated primary users of an OPN library, mathematicians and other interested researchers are the stakeholders in this, to use project management language. While I have a tentative plan for the library, it would not make sense to charge ahead without some feedback from the mathematics community and other stakeholders in this project

1. Bibliography formatting - how important would it be to use AMS vs. APA formatting for the bibliographic entries?
2. Obviously the research articles and other materials directly relating to the OPN conjecture would form the backbone of the library. How helpful would it be to include the works cited by these OPN papers?
3. What closely related topics would be particularly helpful to include?
4. If you have anything else to add to this, let me know.

Thank you in advance for your feedback

ThomRuley 2020-12-14 19:31

I notice a lot of people have read the post, but so far no responses.

Maybe I put too many questions out at once.

A better starting point may be to ask whether anyone else has built or used a specialized library site dedicated to compiling all the available information about a particular math problem. Would this be the first of its kind, or are there others?

sean 2020-12-14 20:28

Since no one else has replied. Way back in the 1990s, I maintained a collection of abstracts in the field of cryptography -- if you try really hard you might still be able to find traces of it. Ultimately, it proved to be a futile effort for several reasons. First, search engines improved to the point where it was simpler to find relevant documents by search rather than a curated list. Second, the rate of new documents was too high to maintain effective manual curation. Third, there was a competing almost overlapping abstract service. Finally, it was always difficult to decide where to draw the line in the scope of the collection.

I'm sure that OPN literature will be considerably smaller, but I imagine these problems will still exist to some degree. Particularly, the final point is likely to be relevant.

What would be more useful, but obviously harder, is a OPN review paper, where you tie the various papers together in a coherent manner. This is useful, because even if you have the abstracts for all the papers, it can be difficult at a glance to determine relevance and how they relate to each other. I do not know enough about this field to know if such a paper already exists.

I'm sorry that this likely sounds negative overall, but in my opinion there are likely better things to spend your time on.

henryzz 2020-12-14 20:38

AFAIK the OPN literature is fairly slow. A review as sean suggests could be very useful. Potentially it could be publishable itself. Certainly, an attempt at sorting out the relevance of each paper would be useful.

pinhodecarlos 2020-12-14 20:47

3 Attachment(s)
Couple of papers in my archives. Check references, search on the web, if not found let me know which ones.


edit:

[URL]https://math.byu.edu/~pace/research.html[/URL]


edit2: The attached pdf's were found googling and "License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use"

CRGreathouse 2020-12-14 21:35

[QUOTE=ThomRuley;565944]Thank you in advance for your feedback[/QUOTE]

Be [url=https://en.wikipedia.org/wiki/Agile_software_development]agile[/url] and build a minimal product before you even think about building in more features. A working library is better than a great concept for a library.

jwaltos 2020-12-15 02:16

Echoing the prior sentiment, build a sandbox where you have considered all the parameters..think of it as existing within a park playground as a start..be it a ghetto, rural or suburban location.

CRGreathouse 2020-12-15 06:45

[QUOTE=ThomRuley;565944]3. What closely related topics would be particularly helpful to include?[/QUOTE]

Obviously anything on the properties of the sigma function is very closely related and would be useful, but you might consider the phi function as well; there's almost a duality between the two functions, though if I could put my finger on it more precisely I'd write a paper describing it. (Or read such a paper, if one exists!)

ThomRuley 2021-01-03 21:03

Thanks for the feedback everybody. After clarifying with my instructor, my school project would me satisfied by migrating the website to a cloud service like AWS. This leaves me with a lot more flexibility in designing the website.

Sean, I like the idea about a review paper. I think I will take a small twist on that and make one or more beginner-friendly guides to the OPN problem. Maybe a listing of all the known conditions an OPN would satisfy, an ELI5 on the sigma chain methods, etc.

CR Greathouse, thanks for the feedback on the tau function. Still trying to get my head around it, but you may be right that there's a connection.

I have thought of a few related topics that would be helpful:
- sigma function
- tau function
- Ore's conjecture (OPN is basically Ore's where H(n)=2, if I read that correctly)
- Integer factorization
- aliqot sequences may be related
- generalized odd numbers

I'll put more in as I think of them.

Thanks again everybody

ThomRuley 2021-01-04 13:40

My bad, the phi function.


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