• Corpus ID: 8544189

Ramanujan series for arithmetical functions

@article{Murty2013RamanujanSF,
  title={Ramanujan series for arithmetical functions},
  author={M. Ram Murty},
  journal={Hardy–Ramanujan Journal},
  year={2013},
  volume={36}
}
  • M. Murty
  • Published 2013
  • Mathematics
  • Hardy–Ramanujan Journal
We give a short survey of old and new results in the theory of Ramanujan expansions for arithmetical functions. 
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31 Citations
Highly Influential Citations
1
Background Citations
10
Methods Citations
4
Results Citations
2

31 Citations

Ramanujan expansions of arithmetic functions of several variables

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Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions

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On Ramanujan expansions and primes in arithmetic progressions

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A note on arithmetical functions with absolutely convergent Ramanujan expansions

Arithmetical functions with absolutely convergent Ramanujan expansions have been recently studied in certain contexts, by the present author, Murty and many others. In this article, we aim to weaken…

On partial sums of arithmetical functions of two variables with absolutely convergent Ramanujan expansions

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On the error term in a Parseval type formula in the theory of Ramanujan expansions II

Twin Primes In Quadratic Arithmetic Progressions

A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the…

Spectral Methods And Prime Numbers Counting Problems

A recent heuristic argument based on basic concepts in spectral analysis showed that the twin prime conjecture and a few other related primes counting problems are valid. A rigorous version of the…

A smooth shift approach for a Ramanujan expansion

All arithmetical functions $F$ satisfying Ramanujan Conjecture, i.e., $F(n)\ll_{\varepsilon}n^{\varepsilon}$, and with $Q-$smooth divisors, i.e., with Eratosthenes transform $F':=F\ast \mu$ supported…

Partial sums of arithmetical functions with absolutely convergent Ramanujan expansions

For an arithmetical function f with absolutely convergent Ramanujan expansion, we derive an asymptotic formula for the sum ∑n≤Nf(n)\documentclass[12pt]{minimal} \usepackage{amsmath}…

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