Results 111 to 120 of about 891 (145)

The Primality of Ramanujan's Tau-Function

The American Mathematical Monthly, 1965
(1965). The Primality of Ramanujan's Tau-Function. The American Mathematical Monthly: Vol. 72, No. sup2, pp. 15-18.
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A generalization of Knopp’s Observation on Ramanujan’s tau-function

The Ramanujan Journal, 2016
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On some exponential sums connected with Ramanujan's τ‐function

Mathematika, 1984
The main results of this paper are: 1) Let \(|\alpha -(a/q)|\leq 1/q^2\), \((a,q)=1\). Then \[ \sum_{n\leq x}\tau(n)\Lambda(n)e(n\alpha) \ll x^{11/2}(xq^{- 1/2}+x^{1/2}q^{1/2}+x^{5/6})\log^cx, \] where \(c>0\) is a suitable constant. 2) If \(R\leq q\leq xR^{-1}\), \(1\leq R\leq x^{1/3}\), \(|\alpha -(a/q)|\leq 1/q^2\) and \((a,q)=1\), then \[ \sum_{n ...
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On Some Relations Involving the Ramanujan’s Tau Function

Indian Journal of Advanced Mathematics
It is known a recurrence relation for the Ramanujan’s tau-function involving the sum of divisors function𝝈(𝒏), whose solution gives a closed formula for 𝝉(𝒏) in terms of complete Bell polynomials, and a determinantal expression for 𝝈(𝒎) where participate the values 𝝉(𝒌).
Dr. R. Sivaraman, Prof. J. López-Bonilla, S. Vidal Beltrán   +2 more
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An alternate proof of a congruence regarding Ramanujan’s tau function

Rendiconti del Circolo Matematico di Palermo, 2004
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On a Diophantine equation involving Fibonacci numbers and the Ramanujan $$\tau $$-function of factorials

, 2022
Florian Luca, Sibusiso Mabaso
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On basic properties of the Ramanujan τ-function

Mathematical Notes, 2011
Let \(\tau (n)\) be the be the Ramanujan \(\tau\)-function. Using the circle method the author proved that for any integer \(N\) the Diophantine equation \[ \sum_{i=1}^{8012}\tau(n_i)=N \] has a solution in positive integers \(n_1,n_2,\dots,n_{8012}\) satisfying the conditions \[ \max_{1\leq i\leq 8012}n_i\ll |N|^{\frac{2}{11}}\,.
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Ramanujan’s Unpublished Manuscript on the Partition and Tau Functions

2012
When Ramanujan died in 1920, he left behind an incomplete, unpublished manuscript in two parts on the partition function p(n) and, in contemporary terminology, Ramanujan’s tau-function τ(n). The influence of this manuscript cannot be underestimated. First, G.H.
George E. Andrews, Bruce C. Berndt
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Generating conjectures on fundamental constants with the Ramanujan Machine

Nature, 2021
Yaron Hadad, Ido Kaminer
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Symplectic Ramanujan Mode Decomposition and its application to compound fault diagnosis of bearings

ISA Transactions, 2022
Yu Yang
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