Related papers: Life and work of the mathemagician Srinivasa Raman…
We derive certain identities involving various known arithmetical functions and a generalized version of Ramanujan sum. L. Toth constructed certain weighted averages of Ramanujan sums with various arithmetic functions as weights. We choose…
We extend the validity range of a Ramanujan's hypergeometric transformation formula proved by Berndt, Bhargava and Garvan, Trans. Amer. Math. Soc. 347, 4163 (1995) and study its implications. Relations to special values of complete elliptic…
In this article we present evaluations of continued fractions studied by Ramanujan. More precisely we give the complete polynomial equations of Rogers-Ramanujan and other continued fractions, using tools from the elementary theory of the…
In his lost notebook, Ramanujan recorded beautiful identities. These include earlier versions of Koshliakov's formula for the divisor function and the transformation formula for the logarithm of Dedekind's $\eta-$function. In this paper we…
We present an infinite family of identities that represent Ramanujan's tau function in terms of convolution sums of twisted divisor functions. Our method involves explicitly constructing non-vanishing level $1$ cusp forms from modular forms…
C.V. Raman (1888-1970) was one of the pioneering scientists to have emerged from India during the colonial era. His scientific explorations were driven by his curiosity to understand wave phenomena. Naturally, optics and related physical…
We study Ramanujan's cubic continued fraction and explicit evaluations of theta-functions
The hypergeometric formulae designed by Ramanujan more than a century ago for efficient approximation of $\pi$, Archimedes' constant, remain an attractive object of arithmetic study. In this note we discuss some $q$-analogues of…
A set S of integers is said to be multiplicative if for every pair m and n of coprime integers we have that mn is in S iff both m and n are in S. Both Landau and Ramanujan gave approximations to S(x), the number of n<=x that are in S, for…
This is a lecture on the ethics and role of science in promoting rational and objective thinking in society. It was delivered by Prof. Shyamal Sengupta of Kolkata, India. Prof. Sengupta, who passed away recently, has inspired generations of…
Mikhail Lomonosov (1711-1765) was the eminent Russian polymath and a towering figure of the European Enlightenment. This English translation of Mikhail Lomonosov seminal work "Oration on the Origin of Light " draws from its original Russian…
Satanandacharya the astronomer and mathematician of 11th century was born in 1068 C.E. at Purusottamdham Puri of Odisha wrote the scripture Bhasvati in 1099 C.E.. The scripture has significant contribution to world of Astronomy and…
The Hardy-Ramanujan formula for the number of integer partitions of $n$ is one of the most popular results in partition theory. While the unabridged final formula has been celebrated as reflecting the genius of its authors, it has become…
This year is the 100th birth anniversary of Richard Philips Feynman. This article commemorates his scientific contributions and lasting legacy.
Narayan Chandra Rana, a person with extraordinary potential from a remote village of Bengal, India, came into the limelight of the international scientific world through his exceptional talent, zeal and courage. In his very short life-span,…
C.S. Seshadri passed away in July 2020. The first part of this article contains some reminiscences from the early 1980s, when as a graduate student in the Tata Institute of Fundamental Research (TIFR), Mumbai, I had the good fortune to…
An asymptotic series in Ramanujan's second notebook (Entry 10, Chapter 3) is concerned with the behavior of the expected value of $\phi(X)$ for large $\lambda$ where $X$ is a Poisson random variable with mean $\lambda$ and $\phi$ is a…
The life of Isaak Yakovlevich Pomeranchuk was short (20.05.1913 -- 14.12.1966). But the impact of his personality and his works on physics and physicists is remarkable. The talk describes the biography of I.Ya. Pomeranchuk, his major…
This article is dedicated to the 80th birthday of the outstanding Georgian and Soviet nuclear physicist Professor R. I. Jibuti (1934-1992).
An overview on Masaki Kashiwara's mathematical work since 1970