Frank Patane

activity

20132015

collaborators

4 papers

math.NT2015

On a generalized identity connecting theta series associated with discriminants $Δ$ and $Δ p^{2}$

Frank Patane

When the discriminants $Δ$ and $Δ p^{2}$ are idoneal, Patane proved a theorem which connects the theta series associated to binary quadratic forms of each discriminant. This paper gen…

math.NT2014

An identity connecting theta series associated with binary quadratic forms of discriminant $Δ$ and $Δ ($ prime $)^{2}$

Frank Patane

We state and prove an identity which connects theta series associated with binary quadratic forms of idoneal discriminants $Δ$ and $Δ p^{2}$ , for $p$ a prime. Employing this identity,…

math.NT2014

Essentially Unique Representations by Certain Ternary Quadratic Forms

Alexander Berkovich, Frank Patane

In this paper we generalize the idea of "essentially unique" representations by ternary quadratic forms. We employ the Siegel formula, along with the complete classification of ima…

math.NT2013

Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients

Alexander Berkovich, Frank Patane

We state and prove an identity which represents the most general eta-products of weight 1 by binary quadratic forms. We discuss the utility of binary quadratic forms in finding a m…

On a generalized identity connecting theta series associated with discriminants Δ and Δp2

An identity connecting theta series associated with binary quadratic forms of discriminant Δ and Δ(prime)2

Essentially Unique Representations by Certain Ternary Quadratic Forms

Binary Quadratic forms and the Fourier coefficients of certain weight 1 eta-quotients

On a generalized identity connecting theta series associated with discriminants $Δ$ and $Δ p^{2}$

An identity connecting theta series associated with binary quadratic forms of discriminant $Δ$ and $Δ ($ prime $)^{2}$