Volume 4 - 1981

1. Progress Towards a conjecture on the mean-value of titchmarsh series-II

The result of this paper may be considered as part II of our earlier paper on Titchmarsh series with the same title. The proof of the main theorem (Theorem 2) depends upon a special case of a convexity theorem of R. M. Gabriel.

2. Some problems of analytic number theory III

The main theme of this paper is to systematize the Hardy-Landau $\Omega$ results and the Hardy $\Omega_{\pm}$ results on the divisor problem and the circle problem. The method of ours is general enough to include the abelian group problem and the results of Richert and the later modifications by Warlimont, and in fact theorem 6 of ours is an improvement of their results. All our results are effective as in our earlier paper II with the same title. Some of our results are new.

3. On series integrals and continued fractions I

This paper deals with the evaluation of a certain continued fraction carried out in an attempt to prove a formula of S. Ramanujan.

4. Addendum and corrigendum to my paper - "One more proof of Siegel's theorem"

In the original paper we noticed a problem with the assertion $L(1,\chi_1)\neq0$ in Lemma 3 of Section 1. The problem is cleared up here. The assertions of the paper all remain valid.