Birthdeath processes and continued fractions
Authors:
Tony Feng, Rachel Kirsch, Elise Villella and Matt Wage
Journal:
Trans. Amer. Math. Soc. 364 (2012), 27032721
MSC (2010):
Primary 03B48; Secondary 11A55
Published electronically:
January 17, 2012
MathSciNet review:
2888225
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Abstract: In the 1997 paper of Parthasarathy, Lenin, Schoutens, and Van Assche, the authors study a birthdeath process related to the RogersRamanujan continued fraction . We generalize their results to establish a correspondence between birthdeath processes and a larger family of continued fractions. It turns out that many of these continued fractions, including , play important roles in number theory, specifically in the theory of modular forms and series. We draw upon the numbertheoretic properties of modular forms to give identities between the transition probabilities of different birthdeath processes.
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Additional Information
Tony Feng
Affiliation:
58 Plympton Street, 479 Quincy Mail Center, Cambridge, Massachusetts 02138
Email:
tfeng@college.harvard.edu
Rachel Kirsch
Affiliation:
7212 Longwood Drive, Bethesda, Maryland 20817
Email:
rkirsch@math.unl.edu
Elise Villella
Affiliation:
146 Harrison Drive, Edinboro, Pennsylvania 16412
Email:
elisemccall@gmail.com
Matt Wage
Affiliation:
1411 N. Briarcliff Drive, Appleton, Wisconsin 54915
Email:
mwage@princeton.edu
DOI:
http://dx.doi.org/10.1090/S00029947201205522X
PII:
S 00029947(2012)05522X
Received by editor(s):
July 24, 2009
Received by editor(s) in revised form:
October 26, 2010
Published electronically:
January 17, 2012
Article copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
