Volume 18 - 1995

Announcements Obituaries

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1. A large value theorem for $\zeta(s)$.

K Ramachandra.

In this paper, we prove a slight improvement of Huxley's zero-density estimate for $\zeta(s)$ near the line ${\rm Re}(s)=\frac{3}{4}$.

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2. On Riemann zeta-function and allied questions-II

R Balasubramanian ; K Ramachandra.

In this paper, two conjectures on the mean value of Dirichlet polynomials are given and are shown to imply good lower bound for $\int_H^{T+H}\vert\zeta(\frac{1}{2}+it)^k\vert^2\,dt$, uniform in $k$ and independent of $T$.

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3. Is the binomial coefficient $2n \choose n$ square free?

G Velammal.

In this paper, we prove the Erdös conjecture that the binomial coefficient ${2n \choose n}$ is never square free, for all $n>4$.

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