Cyclotomic Integers of Prescribed Absolute Value and the Class Group

Cyclotomic Integers and Finite Geometry

The most powerful method for the study of finite geometries with regular or quasiregular automorphism groups G is to translate their definition into an equation over the integral group ring Z[G] and to investigate this equation by applying complex representations of G. For the definitions and the basic facts, see Section 2. If G is abelian, this approach boils down to proving or disproving the ...

Some Conjectures About Cyclotomic Integers

Cyclotomic Integers, Fusion Categories, and Subfactors

Dimensions of objects in fusion categories are cyclotomic integers, hence number theoretic results have implications in the study of fusion categories and finite depth subfactors. We give two such applications. The first application is determining a complete list of numbers in the interval (2, 76/33) which can occur as the FrobeniusPerron dimension of an object in a fusion category. The smalles...

Approximation of Complex Numbers by Cyclotomic Integers

We present a new method of approximating complex numbers by cyclotomic integers in Ze 2i=2 n ] whose coeecients with respect to the basis given by powers of e 2i=2 n are bounded in absolute value by a given integer M. It has been suggested by Cozzens and Finkelstein 5] that such approximations reduce the dynamic range requirements of the discrete Fourier transform. For xed n our algorithm gives...

A note on unique solvability of the absolute value equation

It is proved that applying sufficient regularity conditions to the interval matrix $[A-|B|,A + |B|]$, we can create a new unique solvability condition for the absolute value equation $Ax + B|x|=b$, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive deniteness of a certain point matrix...