Ramanujan mantra, Jan 10, 2023 · Here, the term "inexplicit" means that we can point to particular graphs and show that they are Ramanujan, but there is no known algorithm to construct these graphs (e. A more optimized approach using the recursive function p (k, n) reduces the calculations to 19,900, significantly improving efficiency. So it is perhaps not surprising that he was aware that $1729$ was a sum of cubes in two different ways. He would also have known that $729 = 9^ {3}$. ERH: All zeros of L-functions to complex Dirichlet characters of finite cyclic groups within the critical strip lie on the critical line. . Ramanujan's work. if the graphs are given as quotients of an infinite tree by a particular infinite group). Nov 21, 2020 · So Berndt doesn't consider the Brocard-Ramanujan problem to be a "remaining conjecture" of Ramanujan, I guess? Or maybe he was considering only "formulas" because you were limiting yourself to formulas? Dec 13, 2017 · Here is a mistake which was even featured in the Ramanujan movie: in his letters to Hardy, Ramanujan claimed to have found an exact formula for the prime counting function $\pi (n)$, but (in Hardy's words) Ramanujan’s theory of primes was vitiated by his ignorance of the theory of functions of a complex variable. g. There also aren't many positive integer cubes less than $1729$. Related Article: The History and Importance of the Riemann Hypothesis The goal of this article is to provide the Dec 21, 2020 · Ramanujan's Master Formula: A proof and relation to umbral calculus Asked 5 years, 1 month ago Modified 1 year, 8 months ago Viewed 2k times Since Ramanujan was from India, which presumably used Imperial measures at the time, he would probably have been taught at school that there were $1728$ cubic inches in a cubic foot. Apr 4, 2022 · Riemann Hypothesis and Ramanujan’s Sum Explanation RH: All non-trivial zeros of the Riemannian zeta-function lie on the critical line. Nov 21, 2020 · So Berndt doesn't consider the Brocard-Ramanujan problem to be a "remaining conjecture" of Ramanujan, I guess? Or maybe he was considering only "formulas" because you were limiting yourself to formulas? Dec 13, 2017 · Here is a mistake which was even featured in the Ramanujan movie: in his letters to Hardy, Ramanujan claimed to have found an exact formula for the prime counting function $\pi (n)$, but (in Hardy's words) Ramanujan’s theory of primes was vitiated by his ignorance of the theory of functions of a complex variable. The initial brute force method requires 80,102 calculations, which is inefficient. Mar 23, 2014 · Why was Ramanujan interested in the his tau function before the advent of modular forms? The machinery of modular forms used by Mordel to solve the multiplicative property seems out of context unti Apr 10, 2016 · The forum discussion focuses on the brute force calculation of the number of partitions of 200, as explored by Major MacMahon in the context of S. Although Ramanujan mentions a process where this expression can be obtained from a modular equation of degree $29$, but due to the complexity of Russell's modular equation of degree $29$ I can't apply the technique. "Explicit" means that there is moreover an efficient algorithm to construct the graphs. And note that the processes of calculus were also a part of algebraic manipulation for him. The Jun 20, 2020 · Ramanujan had a great skill in algebraic manipulation (much better than current symbolic software). Almost all his independent (of Hardy) work is based on algebraic manipulation.


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