59 research outputs found
Harnessing Health Care Markets for the Public Interest: Insights for U.S. Health Reform From the German and Dutch Multipayer Systems
Outlines how the German and Dutch systems offer universal coverage via competing insurance plans and promote effective and efficient care. Highlights insurance exchanges, multipayer policies and group purchasing, information systems, and public reporting
Partial theta functions and mock modular forms as q-hypergeometric series
Ramanujan studied the analytic properties of many -hypergeometric series.
Of those, mock theta functions have been particularly intriguing, and by work
of Zwegers, we now know how these curious -series fit into the theory of
automorphic forms. The analytic theory of partial theta functions however,
which have -expansions resembling modular theta functions, is not well
understood. Here we consider families of -hypergeometric series which
converge in two disjoint domains. In one domain, we show that these series are
often equal to one another, and define mock theta functions, including the
classical mock theta functions of Ramanujan, as well as certain combinatorial
generating functions, as special cases. In the other domain, we prove that
these series are typically not equal to one another, but instead are related by
partial theta functions.Comment: 13 page
The probability that the number of points on the Jacobian of a genus 2 curve is prime
In 2000, Galbraith and McKee heuristically derived a formula that estimates
the probability that a randomly chosen elliptic curve over a fixed finite prime
field has a prime number of rational points. We show how their heuristics can
be generalized to Jacobians of curves of higher genus. We then elaborate this
in genus 2 and study various related issues, such as the probability of
cyclicity and the probability of primality of the number of points on the curve
itself. Finally, we discuss the asymptotic behavior as the genus tends to
infinity.Comment: Minor edits, 37 pages. To appear in Proceedings of the London
Mathematical Societ
Almost harmonic Maass forms and Kac-Wakimoto characters
We resolve a question of Kac, and explain the automorphic properties of
characters due to Kac-Wakimoto pertaining to sl(m|n)^ highest weight modules,
for n \geq 1. We prove that the Kac-Wakimoto characters are essentially
holomorphic parts of certain generalizations of harmonic weak Maass forms which
we call "almost harmonic Maass forms". Using a new approach, this generalizes
prior work of the first author and Ono, and the authors, both of which treat
only the case n = 1. We also provide an explicit asymptotic expansion for the
characters.Comment: To appear in J. Reine Angew. Math. (Crelle's Journal). This final
version updates prior arXiv submission 1112.472
Quantum mock modular forms arising from eta-theta functions
In 2013, Lemke Oliver classified all eta-quotients which are theta functions.
In this paper, we unify the eta-theta functions by constructing mock modular
forms from the eta-theta functions with even characters, such that the shadows
of these mock modular forms are given by the eta-theta functions with odd
characters. In addition, we prove that our mock modular forms are quantum
modular forms. As corollaries, we establish simple finite hypergeometric
expressions which may be used to evaluate Eichler integrals of the odd
eta-theta functions, as well as some curious algebraic identities.Comment: 33 page
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