Featured Research

from universities, journals, and other organizations

Glimpses Of A New Mathematical World

Date:
March 17, 2008
Source:
American Institute of Mathematics
Summary:
A new mathematical object, long know to exist but never seen, had its first sighting yesterday. Two researchers have exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics.

A new mathematical object was revealed yesterday during a lecture at the American Institute of Mathematics (AIM). Two researchers from the University of Bristol exhibited the first example of a third degree transcendental L-function. These L-functions encode deep underlying connections between many different areas of mathematics.

The news caused excitement at the AIM workshop attended by 25 of the world's leading analytic number theorists. The work is a joint project between Ce Bian and his adviser, Andrew Booker. Booker commented that, "This work was made possible by a combination of theoretical advances and the power of modern computers." During his lecture, Bian reported that it took approximately 10,000 hours of computer time to produce his initial results.

"This breakthrough opens a door to the study of higher degree L-functions," said Dennis Hejhal, Professor of Mathematics at the University of Minnesota and Uppsala University.

"It's a big advance' added Harold Stark of the University of California, San Diego, who, 30 years ago was the first to accurately calculate second degree transcendental L-functions.

"I thought we were years away from doing this. The geometry of what you have to do and the scale of the computation are orders of magnitude harder."

There are two types of L-functions: algebraic and transcendental, and these are classified according to their degree. The Riemann zeta-function is the grand-daddy of all L-functions. It holds the secret to how the prime numbers are distributed, and is a first-degree algebraic L-function.

The Riemann Hypothesis, announced in 1859 and today the most important of all unsolved math problems, is an example of something that should be true for EVERY L-function. Michael Rubinstein from the University of Waterloo, a participant at the workshop, quickly tested and confirmed the Riemann Hypothesis for the first few zeroes of this newly minted L-function.

Rubinstein, along with William Stein of the University of Washington, will direct a new initiative to chart all L-functions; this project has been recommended for funding by the National Science Foundation. "The techniques developed by Bian and Booker open up whole new possibilities for experimenting with these powerful and mysterious functions and are a key step towards making our group project a success." Rubinstein added.

"It's a big step toward our understanding the 'world of L', which is where most of the secrets of number theory are kept." said Brian Conrey, Director of AIM.

Dorian Goldfeld, Professor of Mathematics at Columbia University summarized the excitement, saying "This discovery is analogous to finding planets in remote solar systems. We know they are out there, but the problem is to detect them and determine what they look like. It gives us a glimpse of new worlds."


Story Source:

The above story is based on materials provided by American Institute of Mathematics. Note: Materials may be edited for content and length.


Cite This Page:

American Institute of Mathematics. "Glimpses Of A New Mathematical World." ScienceDaily. ScienceDaily, 17 March 2008. <www.sciencedaily.com/releases/2008/03/080313124415.htm>.
American Institute of Mathematics. (2008, March 17). Glimpses Of A New Mathematical World. ScienceDaily. Retrieved September 19, 2014 from www.sciencedaily.com/releases/2008/03/080313124415.htm
American Institute of Mathematics. "Glimpses Of A New Mathematical World." ScienceDaily. www.sciencedaily.com/releases/2008/03/080313124415.htm (accessed September 19, 2014).

Share This



More Computers & Math News

Friday, September 19, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

How Much Privacy Protection Will Google's Android L Provide?

How Much Privacy Protection Will Google's Android L Provide?

Newsy (Sep. 19, 2014) Google's local encryption will make it harder for law enforcement or malicious actors to access the contents of devices running Android L. Video provided by Newsy
Powered by NewsLook.com
Virtual Reality Headsets Unveiled at Tokyo Game Show

Virtual Reality Headsets Unveiled at Tokyo Game Show

AFP (Sep. 18, 2014) Several companies unveiled virtual reality headsets at the Tokyo Game Show, Asia's largest digital entertainment exhibition. Duration: 00:48 Video provided by AFP
Powered by NewsLook.com
What HealthKit Bug Means For Your iOS Fitness Apps

What HealthKit Bug Means For Your iOS Fitness Apps

Newsy (Sep. 18, 2014) Apple has delayed the launch of the HealthKit app platform, citing a bug. Video provided by Newsy
Powered by NewsLook.com
Apple's iOS8 Includes New 'Killswitch' To Curb Theft

Apple's iOS8 Includes New 'Killswitch' To Curb Theft

Newsy (Sep. 18, 2014) Apple's new operating system, iOS 8, comes with Apple's killswitch feature already activated, unlike all the models before it. Video provided by Newsy
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile: iPhone Android Web
Follow: Facebook Twitter Google+
Subscribe: RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins