CM periods, CM regulators and hypergeometric functions, II

Traces of Cm Values of Modular Functions

Zagier proved that the traces of singular moduli, i.e., the sums of the values of the classical j-invariant over quadratic irrationalities, are the Fourier coefficients of a modular form of weight 3/2 with poles at the cusps. Using the theta correspondence, we generalize this result to traces of CM values of (weakly holomorphic) modular functions on modular curves of arbitrary genus. We also st...

Petal Width, Cm Petal Width, Cm

There are several reasons why this book might be of interest to a TEX user. First, LTEX has a prominent place in the book. Second, the book describes a very interesting offshoot of literate programming, a topic traditionally popular in the TEX community. Third, since a number of TEX users work with data analysis and statistics, R could be a useful tool for them. Since some TUGboat readers are l...

Final Report: ECE 892(851) The CM-1, CM-2, and CM-5: A Comparative Study

2 Overview of the CM - 2 and CM - 5 Computers

This paper presents a preliminary experimental study of the performance of basic sparse matrix computations on the CM-200 and the CM-5. We concentrate on examining various ways of performing general sparse matrix-vector operations and the basic primitives on which these are based. We compare various data structures for storing sparse matrices and their corresponding matrix – vector operations. ...

CM Jacobians

1. Complex multiplication. We say an abelian variety A of dimension g over a field K admits sufficiently many Complex Multiplications (smCM) if D = End(A) contains a commutative semi-simple algebra Λ ⊂ D of rank dimQ(Λ) = [Λ : Q] = 2g. In this case we say A is a CM abelian variety. A point z ∈ Ag(k) is called a CM point if z is the moduli point of a polarized abelian variety z = [(A,μ)] such th...