Mathematicians trace source of Rogers-Ramanujan identities, find algebraic gold

By Carol Clark | eScienceCommons | May 2, 2014

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Nautilus shell spirals are among the many forms in nature that can be related to the golden ratio, the most famous algebraic number of them all. Mathematicians have discovered a new treasure trove of algebraic numbers and formulas to access them.

Mathematicians have found a framework for the celebrated Rogers-Ramanujan identities and their arithmetic properties, solving another long-standing mystery stemming from the work of Indian math genius Srinivasa Ramanujan.

The findings, by mathematicians at Emory University and the University of Queensland, yield a treasure trove of algebraic numbers and formulas to access them.

"Algebraic numbers are among the first numbers you encounter in mathematics," says Ken Ono, a number theorist at Emory "And yet, it’s surprisingly difficult to find functions that return them as values in a uniform and systematic way."

Ono is the co-author of the new findings, along with S. Ole Warnaar of the University of Queensland and Michael Griffin, an Emory graduate student.

Ono announced the findings in April as a plenary speaker at the Applications of Automorphic Forms in Number Theory and Combinatorics conference at Louisiana State University. He will also present them as a plenary speaker at the 2015 Joint Mathematics Meetings, the largest mathematics meeting in the world, set for January in San Antonio. Warnaar, Griffin and others will give additional talks on the findings during an invited special session to accompany Ono’s plenary address.

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