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1951•Mathematical Proceedings of the Cambridge Philosophical SocietyRequires access

On the order of magnitude of Ramanujan's arithmetical function τ(n)

W. B. Pennington

Open publisher page 8 citations

Abstract

1. In his paper ‘On certain arithmetical functions' Ramanujan (23) considers the function τ(n) defined by the expansion This function appears in the discussion of an asymptotic formula for the function and also in Ramanujan's formula for the number of representations of an integer as the sum of 24 squares. It is also of interest as the coefficient in the expansion of g(z), which plays an important part in the theory of modular functions.

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What this paper is about

1. In his paper ‘On certain arithmetical functions' Ramanujan (23) considers the function τ(n) defined by the expansion This function appears in the discussion of an asymptotic formula for the function and also in Ramanujan's formula for the number of representations of an integer as the sum of 24 squares. It is also of interest as the coefficient in the expansion of g(z), which plays an important part in the theory of modular functions.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

1. In his paper ‘On certain arithmetical functions' Ramanujan (23) considers the function τ(n) defined by the expansion This function appears in the discussion of an asymptotic formula for the function and also in Ramanujan's formula for the number of representations of an integer as the sum of 24 squares. It is also of interest as the coefficient in the expansion of g(z), which plays an important part in the theory of modular functions.

Key concepts: Ramanujan's sum, Arithmetic function, Mathematics, Ramanujan theta function, Ramanujan tau function, Divisor function, Function (biology), Order (exchange)

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