The Shintani–Faddeev modular cocycle
Document Type
Lecture
Publication Date
5-2-2023
Abstract
We ask the question, “how does the infinite q-Pochhammer symbol transform under modular transformations?” and connect the answer to that question to the Stark conjectures. The infinite q-Pochhammer symbol transforms by a generalized factor of automorphy, or modular 1-cocycle, that is analytic on a cut complex plane. This “Shintani-Faddeev modular cocycle” is an SL2(ℤ)-parametrized family of functions generalizing Shintani’s double sine function and Faddeev’s noncompact quantum dilogarithm. We relate real multiplication values of the Shintani–Faddeev modular cocycle to exponentials of certain derivative L-values, conjectured by Stark to be algebraic units generating abelian extensions of real quadratic fields.
Relational Format
presentation
Recommended Citation
Kopp, Gene, "The Shintani–Faddeev modular cocycle" (2023). Algebra/Number Theory Seminar. 2.
https://egrove.olemiss.edu/math_algebra_number_theory/2
