Albert Leon Whiteman

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where [x] denotes, as usual, the greatest integer not exceeding x. D. H. Lehmer [3] has investigated these sums on the basis of a different expression for the roots of unity involved. In the first place he factored the Akin) according to the prime powers contained in k. Secondly, by reducing them to sums studied by H. D. Kloosterman [4] and H. Salie [5], he(More)
We give a formulation, via (1, 1) matrices, of Mathon's construction for conference matrices and derive a new family of conference matrices of order 5·92r+1 + 1, t ≥ 0. This family produces a new conference matrix of order 3646 and a new Hadamard matrix of order 7292. In addition we construct new families of Hadamard matrices of orders 6.92r+1+ 2, 10.92t+1(More)
An Hadamard matrix is a square matrix of ones and minus ones whose row (and therefore column) vectors are orthogonal. The order m of such a matrix is necessarily 1, 2 or is divisible by 4. It is an outstanding conjecture that an Hadamard matrix always exists for m = 412, n any positive integer. Constructions have been given for particular values of n and(More)
It has been conjectured that iϊ-matrices and even skew iJ-matrices always exist for n divisible by 4. Constructions of both types of matrices have been given for particular values of n and also for various infinite classes of values (see [1] for the pertinent references). In [1] D. Blatt and G. Szekeres constructed for the first time a skew ίf-matrix of(More)
Let v, k and * be positive integers. A (v, k, *) cyclic difference set is a set D=[d1 , d2 , ..., dk] of k distinct residues (mod v) such that for each a 0 (mod v) the congruence di&dj #a (mod v) has exactly * distinct solution pairs (di , dj), di , dj # D. Let v=mn. In 1963 Butson [1] generalized cyclic difference sets by considering difference sets(More)
has played an increasingly important role in the analytic theory of numbers. The dash ' beside the summation symbol indicates that the letter of summation runs only through a reduced residue system with respect to the modulus. The number h is defined as any solution of the congruence hh = l (mod k), and n denotes an arbitrary integer. It was shown by Salie(More)
after a lengthy struggle with cancer. He is survived by his devoted family: his wife Sally, his brother and sister-in-law, Irvin and Shirley, and nieces and nephews. Al, as he was known to his colleagues at USC, was born February 15, 1915, in Philadelphia, PA. Sally and Al met on September 1, 1944, while they were serving in the Navy. They were married on(More)