4 citations · 5 across the 14 of their papers we have counts for
5 papers · 1 filter
Constancy of an Infinite Cyclotomic Product via Ramanujan Sums
Hartosh Singh Bal
We show that the infinite product defined by \[ P(z) = -\prod_{n=1}^{\infty} (Φ_n(z))^{-1/n}, \] where \( Φ_n(z) \) is the \( n \)-th cyclotomic polynomial, is constant inside the…
Dold-Gauss Congruences, Norm Descent, and Rational Rigidity
Hartosh Singh Bal
We develop a Witt--Hadamard calculus for Euler products that unifies the classical Gauss congruences with their modern refinement, the Dold congruences. Within this framework we pr…
An easy proof of Ramanujan's famous congruences
Hartosh Singh Bal, Gaurav Bhatnagar
We present a proof of Ramanujan's congruences The proof only requires a limiting case of Jacobi's triple product…
Persistent Quantum Memory in Iterated Lifts
Hartosh Singh Bal
We study quantum coherence in continuous-time quantum walks on perfect graphs generated by the symmetric lift , a canonical, unweighted, undirected constructio…
Perfecting the Line Graph
Hartosh Singh Bal
We study the doubled edge-stage lift \[ \HL'_2(G)=L(G\otimes K_2), \] the line graph of the canonical bipartite double cover of a graph \(G\). The natural involution \((u,v)\leftri…