Quantum Jacobi forms and balanced unimodal sequences
نویسندگان
چکیده
منابع مشابه
Unimodal Sequences and Quantum and Mock Modular Forms
We show that the rank generating function U(t; q) for strongly unimodal sequences lies at the interface of quantum modular forms and mock modular forms. We use U(−1; q) to obtain a quantum modular form which is “dual” to the quantum form Zagier constructed from Kontsevich’s “strange” function F (q). As a result we obtain a new representation for a certain generating function for L-values. The s...
متن کاملQuantum Jacobi forms and finite evaluations of unimodal rank generating functions
In this paper, we introduce the notion of a quantum Jacobi form, and offer the two-variable combinatorial generating function for ranks of strongly unimodal sequences as an example. We then use its quantum Jacobi properties to establish a new, simpler expression for this function as a two-variable Laurent polynomial when evaluated at pairs of rational numbers. Our results also yield a new expre...
متن کاملUnimodal Sequences and “strange” Functions: a Family of Quantum Modular Forms
In this paper, we construct an infinite family of quantum modular forms from combinatorial rank “moment” generating functions for strongly unimodal sequences. The first member of this family is Kontsevich’s “strange” function studied by Zagier. These results rely upon the theory of mock Jacobi forms. As a corollary, we exploit the quantum and mock modular properties of these combinatorial funct...
متن کاملThe Mordell Integral, Quantum Modular Forms, and Mock Jacobi Forms
It is explained how the Mordell integral ∫ R e −2πzx cosh(πx) dx unifies the mock theta functions, partial (or false) theta functions, and some of Zagier’s quantum modular forms. As an application, we exploit the connections between q-hypergeometric series and mock and partial theta functions to obtain finite evaluations of the Mordell integral for rational choices of τ and z. 1. The Mordell In...
متن کاملOzeki Polynomials and Jacobi Forms
A Jacobi polynomial was introduced by Ozeki. It corresponds to the codes over F2. Later, Bannai and Ozeki showed how to construct Jacobi forms with various index using a Jacobi polynomial corresponding to the binary codes. It generalizes Broué-Enguehard map. In this paper, we study Jacobi polynomial which corresponds to the codes over F2f . We show how to construct Jacobi forms with various ind...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.10.022