R Balasubramanian
Articles written in Proceedings – Mathematical Sciences
Volume 93 Issue 2-3 December 1984 pp 101-107
Mean-value of the Riemann zeta-function on the critical line
R Balasubramanian K Ramachandra
This is an expository article. It is a collection of some important results on the meanvalue of$$\left| {\zeta (\frac{1}{2} + it)} \right|.$$
Volume 95 Issue 1 September 1986 pp 31-36
Effect of aspect ratio on the meridional circulation of a rotating homogeneous fluid
V Somaraju D A Mohandas R Balasubramanian
The effect of aspect ratio on the meridional circulation of a homogeneous fluid is analyzed. Aspect ratio is allowed to range between zero and unity. Relationships between possible horizontal and vertical length scales are obtained by length scale analysis as well as by solving an idealized problem. It is found that when
Volume 102 Issue 1 April 1992 pp 1-12
On the frequency of Titchmarsh’s phenomenon for ζ(s)-VIII
R Balasubramanian K Ramachandra A Sankaranarayanan
For suitable functions
Volume 102 Issue 2 August 1992 pp 83-91
Proof of some conjectures on the mean-value of Titchmarsh series — III
R Balasubramanian K Ramachandra
With some applications in view, the following problem is solved in some special case which is not too special. Let
Volume 104 Issue 1 February 1994 pp 167-176 Obituary note
On the zeros of a class of generalised Dirichlet series-XIV
R Balasubramanian K Ramachandra
We prove a general theorem on the zeros of a class of generalised Dirichlet series. We quote the following results as samples.
Volume 108 Issue 2 June 1998 pp 95-108
On Ramanujan asymptotic expansions and inequalities for hypergeometric functions
In this paper we first discuss refinement of the Ramunujan asymptotic expansion for the classical hypergeometric functions
Volume 118 Issue 2 May 2008 pp 183-188 Research Articles
Some Zero-Sum Constants with Weights
S D Adhikari R Balasubramanian F Pappalardi P Rath
For an abelian group 𝐺, the Davenport constant $D(G)$ is defined to be the smallest natural number 𝑘 such that any sequence of 𝑘 elements in 𝐺 has a non-empty subsequence whose sum is zero (the identity element). Motivated by some recent developments around the notion of Davenport constant with weights, we study them in some basic cases. We also define a new combinatorial invariant related to $(\mathbb{Z}/n\mathbb{Z})^d$, more in the spirit of some constants considered by Harborth and others and obtain its exact value in the case of $(\mathbb{Z}/n\mathbb{Z})^2$ where 𝑛 is an odd integer.
Volume 123 Issue 1 February 2013 pp 19-25
Density of Primes in 𝑙-th Power Residues
R Balasubramanian Prem Prakash Pandey
Given a prime number 𝑙, a finite set of integers $S=\{a_1,\ldots,a_m\}$ and 𝑚 many 𝑙-th roots of unity $\zeta^{r_i}_l,i=1,\ldots,m$ we study the distribution of primes 𝑝 in $\mathbb{Q}(\zeta_l)$ such that the 𝑙-th residue symbol of $a_i$ with respect to 𝑝 is $\zeta^{r_i}_l$, for all 𝑖. We find out that this is related to the degree of the extension $\mathbb{Q}\left(a^{\frac{1}{l}}_1,\ldots,a^{\frac{1}{l}}_m\right)/\mathbb{Q}$. We give an algorithm to compute this degree. Also we relate this degree to rank of a matrix obtained from $S=\{a_1,\ldots,a_m\}$. This latter argument enables one to describe the degree $\mathbb{Q}\left(a^{\frac{1}{l}}_1,\ldots,a^{\frac{1}{l}}_m\right)/\mathbb{Q}$ in much simpler terms.
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