Document Type
Lecture
Publication Date
11-7-2008
Abstract
In 1969, L. Winquist gave an elementary proof of Ramanujan's congruence p(11n+6)=0 (mod 11), where p(n) is the number of partitions of the positive integer n. An identity later named after him plays a vital role in his proof. We give an elementary proof of this identity in this talk. We begin with the left side of Winquist's identity, find all its zeros as a function of two variables, then construct a product of theta functions with the same zeros. By considering functional relations, we show that the quotient of the two functions is an analytic function, then prove the quotient is a constant by taking special values of both functions. This method can also be applied to prove many other interesting theta function identities.
Relational Format
presentation
Recommended Citation
Cao, Zhu, "A new proof of Winquist’s Identity" (2008). Algebra/Number Theory Seminar. 52.
https://egrove.olemiss.edu/math_algebra_number_theory/52
