Ramanujan Movie

When exploring ramanujan movie, it's essential to consider various aspects and implications. 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. 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. This perspective suggests that, related Article: The History and Importance of the Riemann Hypothesis The goal of this article is to provide the ...

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. Another key aspect involves, 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 $\mathbb {Q} (\sqrt {-163})$. Deligne's proof of Ramanujan's conjecture - MathOverflow.

I am trying to understand Deligne's proof of the Ramanujan conjecture and more generally how one associates geometric objects (ultimately, motives) to modular forms. As the first step, which I Building on this, 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

Explicit constructions of Ramanujan graphs - MathOverflow. 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.g. Building on this, if the graphs are given as quotients of an infinite tree by a particular infinite group).

"Explicit" means that there is moreover an efficient algorithm to construct the graphs. nt.number theory - On Ramanujan's tau function - MathOverflow. Building on this, @Zhi-WeiSun The vanishing of Ramanujan’s function, D.

Lehmer It appears Lehmer’s interest stems from the fact that Tau function is generated from powers of Lacunary Series and it is of interest to investigate whether powers of lacunary series also have many zero coefficients.