2019
Том 71
№ 9

All Issues

Bhargava S.

Articles: 2
Article (English)

On Some Ramanujan Identities for the Ratios of Eta-Functions

Bhargava S., Rajanna K. R., Vasuki K. R.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 8. - pp. 1011–1028

We give direct proofs of some of Ramanujan’s P-Q modular equations based on simply proved elementary identities from Chapter 16 of his Second Notebook.

Article (English)

A modular transformation for a generalized theta function with multiple parameters

Bhargava S., Mahadeva Naika M. S., Maheshkumar M. C.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2009. - 61, № 8. - pp. 1040-1052

We obtain a modular transformation for the theta function $$∑_{-∞}^{∞}∑_{-∞}^{∞}q^{a(m^2 + m^n) + cn^2 + λm + μn + ν_{ς}Am + Bn_{Z}Cm + Dn},$$ which enables us to unify and extend several modular transformations known in literature.