Quadratic Forms and Four Partition Functions Modulo 3

Quadratic Functions, Optimization, and Quadratic Forms

Quadratic Forms and Height Functions

Applications of quadratic D-forms to generalized quadratic forms

In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.

Periodicities of Partition Functions and Stirling Numbers modulo

If p(n, k) is the number of partitions of n into parts <k. then the sequence { p(k, li), p(k + 1, Ii)....} is periodic modulo a prime p. We find the minimum period Q = Q(li, p) of this sequence. More generally, we find the minimum period, modulo P, of {pW Vi,,,. the number of partitions of n whose parts all lie in a fixed finite set T of positive integers. We find the minimum period, module p, ...

Gold and Kasami-Welch functions, quadratic forms, and bent functions

We use elementary facts about quadratic forms in characteristic 2 to evaluate the sign of some Walsh transforms in terms of a Jacobi symbol. These results are applied to the Walsh transforms of the Gold and KasamiWelch functions. We prove that the Gold functions yield bent functions when restricted to certain hyperplanes. We also use the sign information to determine the dual bent function.