Note on Hermitian Jacobi Forms

We compare the spaces of Hermitian Jacobi forms (HJF) of weight $k$ and indices $1,2$ with classical Jacobi forms (JF) of weight $k$ and indices $1,2,4$. Using the embedding into JF, upper bounds for the order of vanishing of HJF at the origin is obtained. We compute the rank of HJF as a module over elliptic modular forms and prove the algebraic independence of the generators in case of index 1. Some related questions are discussed.Comment: 24 pages; title changed, abstract changed, some proofs expanded and new results adde

The Procedural Due Process Requirements for No-Fly Lists

[Excerpt] “Imagine arriving at the airport and checking in at the ticketing booth. You tell the ticketing agent your name, your flight number, and show the agent your identification. The agent enters the information into the terminal and a look of shock appears on his or her face. While other passengers are waiting behind you, the agent calls for security and mentions in front of other passengers that you are denied from boarding the plane. Now imagine that you are a famous United States senator arriving from a political convention and the ticketing agent tells you that you cannot board a plane because your name appears in a database. Or imagine that you are an ACLU lawyer who spoke at a conference concerning terrorism and are denied boarding because your name appears in a database. Or imagine that you are a former pop star singer who converted to Islam and are denied boarding a plane. Whether you are a leisure traveler, a political figurehead, a professional business traveler, or popular figure in society, the security measures for air travel in this post 9/11 era affect everyone. […] This article will focus on why placing an individual’s name on a No-Fly or Selectee List without prior notice or a hearing is a violation of the Fifth Amendment’s due process clause. Part II will provide a general background of the Transportation Security Administration and the agency’s authority to generate the No-Fly and the Selectee Lists. Part III will focus on why placing passengers on one of the lists deprives them of their right to interstate travel and reputation sufficient to invoke the Fifth Amendment’s due process clause. Part IV will discuss why passengers are entitled to notice and a hearing prior to placement of their names on the lists and the requirements for a constitutionally adequate hearing.

Finiteness of simple holomorphic eta quotients of a given weight

We provide a simplified proof of Zagier's conjecture / Mersmann's theorem which states that of any particular weight, there are only finitely many holomorphic eta quotients, none of which is an integral rescaling of another eta quotient or a product of two holomorphic eta quotients other than 1 and itself.Comment: 14 pages. arXiv admin note: text overlap with arXiv:1602.02835, arXiv:1602.03087, arXiv:1602.0281

Irrational behavior of algebraic discrete valuations

We study algebraic discrete valuations dominating normal local domains of dimension two. We construct a family of examples to show that the Hilbert-Samuel function of the associated graded ring of the valuation can fail to be asymptotically of the form: quasi-polynomial plus a bounded function. We also show that the associated multiplicity can be irrational, or even transcendental