{"docId":5105,"paperId":5105,"url":"https:\/\/hrj.episciences.org\/5105","doi":"10.46298\/hrj.2019.5105","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986043","repositoryVersion":1,"repositoryLink":"https:\/\/hal.archives-ouvertes.fr\/hal-01986043v1","dateSubmitted":"2019-01-23 14:13:47","dateAccepted":"2019-01-23 15:29:32","datePublished":"2019-01-23 15:30:10","titles":{"en":"On an identity of Ramanujan"},"authors":["Motohashi\n, \nYoichi"],"abstracts":{"en":"Proofs published so far in articles and books, of the Ramanujan identity presented in this note, which depend on Euler products, are essentially the same as Ramanujan's original proof. In contrast, the proof given here is short and independent of the use of Euler products."},"keywords":[{"en":"Ramanujan's identity"},{"en":"M\u00f6bius inversion"},{"en":"Selberg's ${\\Lambda}^2$-sieve"},"\n[\nMATH\n] \nMathematics [math]","\n[\nMATH.MATH-NT\n] \nMathematics [math]\/Number Theory [math.NT]"]}