LMFDB Database Website

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Message 1791 - Posted: 4 Dec 2016, 16:59:33 UTC
Last modified: 4 Dec 2016, 17:07:10 UTC

Was reading a website article talking about L-functions of which I know nothing about. It then talks about L functions and modular forms database.

http://www.mcgill.ca/newsroom/channels/news/exploring-mathematical-universe-260825
(Article that talks about the link below)

One excerpt from the article:

"Massive computations

The scale of the computational effort involved in the LMFDB is staggering: hundreds of CPU years were involved in compiling the databases, requiring thousands of hours of human effort.

A recent computation by Andrew Sutherland at MIT used 72,000 cores of Google’s Compute Engine to complete in hours a tabulation that would have taken more than a century on a single computer. As noted by Sutherland, “computations in number theory are often amenable to parallelization, and this makes it easy to scale them to the cloud.” The application of large-scale cloud computing to research in pure mathematics is just one of the ways in which the project is pushing forward the frontier of mathematics."


http://www.lmfdb.org/ModularForm/GL2/TotallyReal/

My question is are we contributing to this in some way? I noticed this page
regarding Hilbert Modular forms and some familar things came out including the current project symbol of \Q(\sqrt{2})

I just wanted to see if they are working in parallel to what we are doing or
they are doing something else. It's like a Periodic table for Number Theorists. I'm
sure the admin of the site knows it all too.

Thanks for any help.
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Profile Eric Driver
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Message 1792 - Posted: 4 Dec 2016, 17:42:06 UTC - in response to Message 1791.  

Was reading a website article talking about L-functions of which I know nothing about. It then talks about L functions and modular forms database.

http://www.mcgill.ca/newsroom/channels/news/exploring-mathematical-universe-260825
(Article that talks about the link below)

One excerpt from the article:

"Massive computations

The scale of the computational effort involved in the LMFDB is staggering: hundreds of CPU years were involved in compiling the databases, requiring thousands of hours of human effort.

A recent computation by Andrew Sutherland at MIT used 72,000 cores of Google’s Compute Engine to complete in hours a tabulation that would have taken more than a century on a single computer. As noted by Sutherland, “computations in number theory are often amenable to parallelization, and this makes it easy to scale them to the cloud.” The application of large-scale cloud computing to research in pure mathematics is just one of the ways in which the project is pushing forward the frontier of mathematics."


http://www.lmfdb.org/ModularForm/GL2/TotallyReal/

My question is are we contributing to this in some way? I noticed this page
regarding Hilbert Modular forms and some familar things came out including the current project symbol of \Q(\sqrt{2})

I just wanted to see if they are working in parallel to what we are doing or
they are doing something else. It's like a Periodic table for Number Theorists. I'm
sure the admin of the site knows it all too.

Thanks for any help.


Yes, there is a link between modular forms and number fields. The website you linked to has a section on number fields:
http://www.lmfdb.org/NumberField/
A large portion of that data comes from the Jones/Roberts database. Note that John Jones is my old thesis advisor. Fields that are obtained from this project are fed back to John and incorporated into the database.

You will notice that the lmfdb database is "complete" with respect to certain field properties for lower degree fields. This project deals with degree 10 fields, which are inherently much more difficult to find, and for which the database is currently incomplete. This project has already completed the search over {2,3} and is currently working on {2,5}.
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Message 1793 - Posted: 5 Dec 2016, 3:46:25 UTC - in response to Message 1792.  

Very interesting that your thesis
Advisor is associated with the LMFDB! I think its interesting we are contributing to it and gives me more reason to be glad I chose this project in the BOINC system.

Also what are ramified and unramified primes?
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Message 1794 - Posted: 5 Dec 2016, 4:19:04 UTC - in response to Message 1793.  

Very interesting that your thesis
Advisor is associated with the LMFDB! I think its interesting we are contributing to it and gives me more reason to be glad I chose this project in the BOINC system.

Also what are ramified and unramified primes?


That's a tough one to explain in simple terms. An integer prime will factor in the extension field - if it's factorization contains a square then it is ramified. So for example, if it factors as P^2*Q it is ramified, but if it factors as P*Q it is unramified.

You could probably find a more detailed explanation on the web.
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Message 1795 - Posted: 5 Dec 2016, 7:12:02 UTC - in response to Message 1794.  

Yes thank you Eric, I understand that mathematical lingo is its own language and I am looking up the info now as well. There's a reason why you need years of schooling to understand this stuff. I appreciate it all the more though.

Thanks for the replies.
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