A hardware unit for interval arithmetic (including division by an interval that contains zero) is described in this paper. After a brief introduction an instruction set for interval arithmetic is defined which is attractive from the mathematical point of view. These instructions consist of the basic arithmetic operations and comparisons for intervals including the relevant lattice operations. T...

Let $\sigma$ be a permutation of nonempty finite or countably infinite set $X$ and let $F_X\left( \sigma^k\right)$ count the number fixed points $k$th power $\sigma$. This paper explains how arithmetic function $k \mapsto \left(F_X\left( \sigma^k\right) \right)_{k=1}^{\infty}$ determines conjugacy class $\sigma$, constructs an algorithm to compute from point counting \sigma^k\right)$, describes...

Often p-adic L-functions are the right bridge between these and the arithmetic objects. p-adic L-functions: • These admit no näıve definition. • In general, given M a “motive”or “algebraic automorphic representation”, a p-adic L-function associated with M tends to have two properties: – it interpolates the special values L(n,M ⊗ χ) p-adically, for n in some interval and χa p-power conductor Dir...

In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...