Volume 9 -1986


1. On the frequency of Titchmarsh's phenomenon for ζ(s) IV.

R Balasubramanian.
The inequality in the main theorem of this paper improves on an earlier weaker version by a certain shaper constant.

2. Hybrid mean square of L-functions.

Mangala J Narlikar.
This paper discusses the Dirichlet's L-function L(s,χ) for a character χ mod k, and we prove a refinement of the error term using the result on Hurwitz Zeta function, proved by the author in an earlier paper.

3. The number of finite non-isomorphic abelian groups in mean square.

Aleksandar Ivić.
Let Δ(x)=nxa(n)6j=1cjx1/j denote the error term in the abelian group problem. Using zeta-function methods it is proved that X1Δ2(x)dx << X39/29log2X
where the exponent 39/29=1.344827 is close to the best possible exponent 4/3 in this problem.