G. Bhatnagar

collaborators

2 papers

math.NT2025

An easy proof of Ramanujan's famous congruences $p (5 m + 4) \equiv 0 \equiv τ (5 m + 5) (mod 5)$

Hartosh Singh Bal, Gaurav Bhatnagar

We present a proof of Ramanujan's congruences $p (5 n + 4) \equiv 0 (mod 5) and τ (5 n + 5) \equiv 0 (mod 5) .$ The proof only requires a limiting case of Jacobi's triple product…

math.CA2017

Heine's method and $A_{n}$ to $A_{m}$ transformation formulas

Gaurav Bhatnagar

We apply Heine's method---the key idea Heine used in 1846 to derive his famous transformation formula for $_{2} ϕ_{1}$ series---to multiple basic series over the root system of type $A$ …

An easy proof of Ramanujan's famous congruences p(5m+4)≡0≡τ(5m+5)(mod5)

Heine's method and An​ to Am​ transformation formulas

An easy proof of Ramanujan's famous congruences $p (5 m + 4) \equiv 0 \equiv τ (5 m + 5) (mod 5)$

Heine's method and $A_{n}$ to $A_{m}$ transformation formulas