# Questions tagged [ramanujan]

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### Impact of Ramanujan's Note on a set of simultaneous equations

I had been pointed to Ramanujan's 1912 article Note on a set of simultaneous equations in this answer to my former question about the Solvability of a system of polynomial equations. While the ...
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### Ramanujan's type sum

Is it possible to get a good upper bound for $$\sum_{1\leq |h|\leq q}\frac{c_{q}(a-h)}{h}$$ with $(a,q)=1$ and $1\leq a\leq q$.
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### Ramanujan and his influence on others

A few years ago I saw a paper where a few important researchers were asked which theorem of Ramanujan impressed them most. I don't remember details, but I would like to see this paper again. Details, ...
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### Elliptic functions and "complex multiplication" [closed]

I have before me a copy of "The Indian Mathematician Ramanujan", by G. H. Hardy (not actually related to me, as far as I know), which appeared in volume 44, number 3 (March 1937) of The American ...
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### A partition congruence modulo 13

In the paper "Note on certain modular relations considered by Messrs Ramanujan, Darling and Rogers" (Proceedings of London Mathematical Society (1922) s2-20 (1): 408-416) Mordell gives proofs of the ...
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### Ramanujan's series for $(1/\pi)$ and modular equation of degree $29$

In his famous paper "Modular Equations and Approximations to $\pi$", Ramanujan gives the following famous series for $1/\pi$: \begin{align}\frac{1}{2\pi\sqrt{2}} &= \frac{1103}{99^{2}} + \frac{...
Given the binomial function $\binom{n}{k}$. 1. Define the following sequences, \begin{aligned} u_1(k) &= \tbinom{2k}{k}\tbinom{3k}{k}\tbinom{6k}{3k} = 1, 120, 83160, 81681600,\dots \\ u_2(k) &... 21 votes 0 answers 2k views ### Trigonometry related to Rogers--Ramanujan identities For integers n\ge2 and k\ge2, fix the notation [m]=\sin\frac{\pi m}{nk+1} \quad\text{and}\quad [m]!=\dots[m], \qquad m\in\mathbb Z_{>0}.  Consider the following trigonometric numbers:...
A little background: Let $f(z)=\sum_{n=1}^{\infty} a(n) e^{2\pi i nz}$ be a classical holomorphic cuspidal eigenform on $\Gamma_1(N)$, of weight $k \geq 2$ normalized with $a(1)=1$. The Ramanujan ...