On an arithmetical function

Hershel M. Farkas

doi:10.1007/s11139-004-0141-5

On an arithmetical function

Hershel M. Farkas^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

In this paper we introduce an arithmetical function δ(n) the difference between the number of divisors of n congruent to 1 mod 3 and those congruent to -1 mod 3. This function then is related to the classical function σ(n) which is the sum of the divisors of n. In particular we prove the identity 3(∑_n=0^∞δ(3n+1)xⁿ) ² = ∑_n=0^∞σ(3n+2)xⁿ.

Original language	English
Pages (from-to)	309-315
Number of pages	7
Journal	Ramanujan Journal
Volume	8
Issue number	3
DOIs	https://doi.org/10.1007/s11139-004-0141-5
State	Published - Sep 2004

Keywords

Divisor functions
Theta functions

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10.1007/s11139-004-0141-5

Cite this

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abstract = "In this paper we introduce an arithmetical function δ(n) the difference between the number of divisors of n congruent to 1 mod 3 and those congruent to -1 mod 3. This function then is related to the classical function σ(n) which is the sum of the divisors of n. In particular we prove the identity 3(∑n=0∞δ(3n+1)xn) 2 = ∑n=0∞σ(3n+2)xn.",

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AB - In this paper we introduce an arithmetical function δ(n) the difference between the number of divisors of n congruent to 1 mod 3 and those congruent to -1 mod 3. This function then is related to the classical function σ(n) which is the sum of the divisors of n. In particular we prove the identity 3(∑n=0∞δ(3n+1)xn) 2 = ∑n=0∞σ(3n+2)xn.

KW - Divisor functions

KW - Theta functions

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VL - 8

SP - 309

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JO - Ramanujan Journal

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IS - 3

ER -

On an arithmetical function

Abstract

Keywords

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