Understanding ramanujan movie in english requires examining multiple perspectives and considerations. The unproved formulas of Ramanujan - MathOverflow. 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?
What did Ramanujan get wrong? 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 Extended Riemann Hypothesis and Ramanujan's Sum. Another key aspect involves, riemann Hypothesis and Ramanujan’s Sum Explanation RH: All non-trivial zeros of the Riemannian zeta-function lie on the critical line.
ERH: All zeros of L-functions to complex Dirichlet characters of finite cyclic groups within the critical strip lie on the critical line. From another angle, related Article: The History and Importance of the Riemann Hypothesis The goal of this article is to provide the ... From another angle, ho.history overview - What were Ramanujan's standard tricks/approaches ....
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. And note that the processes of calculus were also a part of algebraic manipulation for him. Ramanujan's series for $ (1/\pi)$ and modular equation of degree $29$.
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. Similarly, how did Ramanujan come up with the Ramanujan summation and is it .... The origin of the Ramanujan's $\pi^4\approx 2143/22$ identity. What is the origin of the Ramanujan's approximate identity $$\pi^4\approx 2143/22,\;\;\tag 1$$ which is valid with $10^ {-9}$ relative accuracy? For comparison, the relative accuracy of the well kno...
Generalizing Ramanujan's "1729 story" - MathOverflow. In relation to this, 6 Whenever I read the anecdote about Hardy, Ramanujan and the taxi number 1729 I'm amazed that it could have occurred to anyone just off the top of their head that 1729 can be written as the sum of two cubes in two different ways -- and that it is the smallest such number. At all events, there are several ways to look at this in a more general way.
fa.functional analysis - Ramanujan's Master Formula: A proof and .... Ramanujan's Master Formula: A proof and relation to umbral calculus Ask Question Asked 4 years, 10 months ago Modified 1 year, 5 months ago This perspective suggests that, the Chudnovskys' original proof of their $1/\pi$ formula. I am trying to understand the famous paper by the Chudnovsky brothers, "Approximations and complex multiplication according to Ramanujan" (reprinted in Pi: A Source Book), which (among other things) contains their formula for $1/\pi$ that is based on the imaginary quadratic field $\mathbb {Q} (\sqrt {-163})$.
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