On an identity of Ramanujan

Yoichi Motohashi (1)

1 Honkomagome

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.

Mots clés: Ramanujan's identity; Möbius inversion; Selberg's ${\Lambda}^2$-sieve

Domaines: Mathématiques [math]; Théorie des nombres [math.NT]

Yoichi Motohashi. On an identity of Ramanujan. Hardy-Ramanujan Journal, 2019, Atelier Digit_Hum, pp.48 - 49. ⟨10.46298/hrj.2019.5105⟩. ⟨hal-01986043⟩