One example is the Ramanujan – Nagell equation, 2 < sup > n </ sup > − 7 = x < sup > 2 </ sup >.

The theoretical foundations for such series is given by Broadhurst ( the first formula ) and Ramanujan ( the second formula ) The algorithms for fast evaluation of the Catalan constant is constructed by E. Karatsuba.

A more rapidly convergent series due to Ramanujan is

The function li ( x ) has a single positive zero ; it occurs at x ≈ 1. 45136 92348 ...; this number is known as the Ramanujan – Soldner constant.

Ramanuja or Ramanujan or Ramanujam is a Tamil name.

The Indian Clerk ( 2007 ) is a novel by David Leavitt based on Hardy's life at Cambridge, including his discovery of and relationship with Srinivasa Ramanujan.

where represents the Ramanujan tau function, and is the divisor function.

In mathematics, the Ramanujan – Soldner constant ( also called the Soldner constant ) is a mathematical constant defined as the unique positive zero of the logarithmic integral function.

It is named after Srinivasa Ramanujan and Johann Georg von Soldner.

the only positive zero of the exponential integral occurs at the natural logarithm of the Ramanujan – Soldner constant, whose value is approximately ln ( μ ) ≈ 0. 372507410781366634461991866 …

Thunchaththu Ramanujan Ezhuthachan ( 17th century ) is considered as the Father of the Malayalam language, because of his influence on the acceptance of the Malayalam alphabet and his extremely popular poetic works like Adhyathmaramayanam.

In 1934 Turán gave a new and very simple proof of a 1917 result of G. H. Hardy and Ramanujan on the normal order of the number of distinct prime divisors of a number n, namely that it is very close to ln ln n. In probabilistic terms he estimated the variance from ln ln n. Halász says " Its true significance lies in the fact that it was the starting point of probabilistic number theory ".

The constant of proportionality is the Landau – Ramanujan constant, which was discovered independently by Edmund Landau and Srinivasa Ramanujan.

The generalized Ramanujan conjecture or Ramanujan – Petersson conjecture, introduced by, is a generalization to other modular forms or automorphic forms.

The more general Ramanujan – Petersson conjecture for holomorphic cusp forms in the theory of elliptic modular forms for congruence subgroups has a similar formulation, with exponent ( k − 1 )/ 2 where k is the weight of the form.

The Ramanujan – Petersson conjecture for Maass wave forms is still open ( as of 2011 ).

suggested that the generalized Ramanujan conjecture should still hold for generic cuspidal automorphic representations of a quasi-split reductive group, where a generic cusp form is roughly one with a Whittaker model.

Lafforgue's theorem implies that the generalized Ramanujan conjecture is true for the general linear group over a global function field, by an argument due to.

Ta ( 2 ), also known as the Hardy – Ramanujan number, was first published by Bernard Frénicle de Bessy in 1657 and later immortalized by an incident involving mathematicians G. H. Hardy and Srinivasa Ramanujan.

It has also been a participant and a winner at the Inter-School Maths Competition and many more other such competitions such as the Sri Srinivasa Ramanujan Maths competition.

Lord Pentland is also remembered for having assisted the Indian mathematician Srinivasa Ramanujan make his journey to England.

The values of b are just those of n − 3, and the corresponding triangular Mersenne numbers ( also known as Ramanujan – Nagell numbers ) are:

In a 1975 April Fool article in Scientific American magazine, " Mathematical Games " columnist Martin Gardner made the ( hoax ) claim that the number was in fact an integer, and that the Indian mathematical genius Srinivasa Ramanujan had predicted it — hence its name.

Indeed, the name " Ramanujan graph " was derived from this connection.

He was born at Trikkantiyur, at the town of Tirur, in Vettathunadu. His individual name is Ramanujan.

:* Ramanujan's congruences, congruences for the partition function, p ( n ), first discovered by Ramanujan in 1919

* S. Ramanujan, ( 1887 – 1920 ), the famous Indian mathematician, known for his work on continued fractions, number theory, and his 1729 observation

Indian mathematician Srinivasa Ramanujan in 1913, C. D. Olds in 1963, Martin Gardner in 1966, and Benjamin Bold in 1982 all gave geometric constructions for

Srinivasa Ramanujan in 1914 gave a ruler-and-compass construction which was equivalent to taking the approximate value for pi to be

The crucial idea of considering even k powers of E was inspired by the paper, who used a similar idea with k = 2 for bounding the Ramanujan tau function.

pointed out that a generalization of Rankin's result for higher even values of k would imply the Ramanujan conjecture, and Deligne realized that in the case of zeta functions of varieties, Grothendieck's theory of zeta functions of sheaves provided an analogue of this generalization.

Ramanujan in his notebooks tried to generalize the Euler product for Zeta function in the form:

For example, the famous Ramanujan function τ ( n ) arises as the sequence of Fourier coefficients of the cusp form of weight 12 for the modular group, with a < sub > 1 </ sub > = 1.

In mathematics, the Landau – Ramanujan constant occurs in a number theory result stating that the number of positive integers less than x that are the sum of two square numbers, for large x, varies as

Hardy and Srinivasa Ramanujan in 1918 obtained the following asymptotic formula for P ( n ):

reformulated the Ramanujan – Petersson conjecture in terms of automorphic representations for GL < sub > 2 </ sub > as saying that the local components of automorphic representations lie in the principal series, and suggested this condition as a generalization of the Ramanujan – Petersson conjecture to automorphic forms on other groups.

Ramanujan bounds for groups other than can be obtained as an application of known cases of Langlands functoriality.

The Ramanujan – Petersson conjecture for general linear groups implies Selberg's conjecture about eigenvalues of the Laplacian for some discrete groups.

In turn, the Ramanujan – Petersson conjecture for general linear groups follows from the Arthur conjectures.

* 1887 – Srinivasa Ramanujan, Indian mathematician ( d. 1920 )

Some notable mathematicians include Archimedes of Syracuse, Leonhard Euler, Carl Gauss, Johann Bernoulli, Jacob Bernoulli, Aryabhata, Brahmagupta, Bhaskara II, Nilakantha Somayaji, Omar Khayyám, Muhammad ibn Mūsā al-Khwārizmī, Bernhard Riemann, Gottfried Leibniz, Andrey Kolmogorov, Euclid of Alexandria, Jules Henri Poincaré, Srinivasa Ramanujan, Alexander Grothendieck, David Hilbert, Alan Turing, von Neumann, Kurt Gödel, Joseph-Louis Lagrange, Georg Cantor, William Rowan Hamilton, Carl Jacobi, Évariste Galois, Nikolay Lobachevsky, Rene Descartes, Joseph Fourier, Pierre-Simon Laplace, Alonzo Church, Nikolay Bogolyubov and Pierre de Fermat.

Starting around the 15th century, new algorithms based on infinite series revolutionized the computation of, and were used by mathematicians including Madhava of Sangamagrama, Isaac Newton, Leonhard Euler, Carl Friedrich Gauss, and Srinivasa Ramanujan.

* April 26 – Srinivasa Ramanujan, Indian mathematician ( b. 1887 )

* December 22 – Srinivasa Aaiyangar Ramanujan, Indian mathematician ( d. 1920 )

Srinivasa Ramanujan wrote about generalisations of the binomial theorem, and earned a reputation as a genius by writing articles that confounded the best extant mathematicians.

Starting in 1914, he was the mentor of the Indian mathematician Srinivasa Ramanujan, a relationship that has become celebrated.

Examples of particularly extreme prodigies could include Wolfgang Amadeus Mozart in music, Magnus Carlsen, Sergey Karjakin, and Judit Polgar in chess, Carl Friedrich Gauss, Srinivasa Ramanujan, John von Neumann, and Terence Tao in mathematics, Pablo Picasso and Wang Ximeng in art, and Saul Kripke in philosophy.

It was first proven by Pafnuty Chebyshev, and a short but advanced proof was given by Srinivasa Ramanujan.

The Srinivasa Ramanujan Complex was incorporated as another academic complex of the institute with Takshashila starting operation in 2002, Vikramshila in 2003 and Nalanda in 2012.

# REDIRECT Srinivasa Ramanujan

# redirect Srinivasa Ramanujan

He interacted with the mathematical genius Srinivasa Ramanujan during the latter's time at Cambridge.

The Indian National Science Academy honoured him with the Srinivasa Ramanujan Medal in 1974.

* December 22 – Srinivasa Ramanujan ( died 1920 ), Indian mathematician.

The concept was first mentioned in 1657 by Bernard Frénicle de Bessy, and was made famous in the early 20th century by a story involving Srinivasa Ramanujan.

Category: Srinivasa Ramanujan