Inequivalence of Difference Sets: On a Remark of Baumert

A Remark on a Remark by Macaulay or Enhancing Lazard Structural Theorem

Inequivalence of Skew Hadamard Difference Sets and Triple Intersection Numbers Modulo a Prime

Recently, Feng and Xiang [10] found a new construction of skew Hadamard difference sets in elementary abelian groups. In this paper, we introduce a new invariant for equivalence of skew Hadamard difference sets, namely triple intersection numbers modulo a prime, and discuss inequivalence between Feng-Xiang skew Hadamard difference sets and the Paley difference sets. As a consequence, we show th...

On the existence of cyclic difference sets with small parameters

Previous surveys by Baumert [3] and Lopez and Sanchez [12] have resolved the existence of cyclic (v, k, λ) difference sets with k ≤ 150, except for six open cases. In this paper we show that four of those difference sets do not exist. We also look at the existence of difference sets with k ≤ 300, and cyclic Hadamard difference sets with v ≤ 10,000. Finally, we extend [6] to show that no cyclic ...

A remark on boundedness of composition operators between weighted spaces of holomorphic functions on the upper half-plane

In this paper, we obtain a sucient condition for boundedness of composition operators betweenweighted spaces of holomorphic functions on the upper half-plane whenever our weights are standardanalytic weights, but they don't necessarily satisfy any growth condition.

A remark on the means of the number of divisors

‎We obtain the asymptotic expansion of the sequence with general term $frac{A_n}{G_n}$‎, ‎where $A_n$ and $G_n$ are the arithmetic and geometric means of the numbers $d(1),d(2),dots,d(n)$‎, ‎with $d(n)$ denoting the number of positive divisors of $n$‎. ‎Also‎, ‎we obtain some explicit bounds concerning $G_n$ and $frac{A_n}{G_n}$.