Mario DeFranco

collaborators

3 papers

math.NT2019

On properties of the Taylor series coefficients of the Riemann xi function at $s = \frac{1}{2}$

Mario DeFranco

We prove some properties about the non-zero Taylor series coefficients $a_{k}$ of the Riemann xi function $ξ (s)$ at $s = \frac{1}{2}$ . In particular, we present integral formulas that…

math.CO2019

A Constructive Proof of Jacobi's Identity for the Sum of Two Squares

Mario DeFranco

We present a constructive proof of Jacobi's identity for the sum of two squares. We present a combinatorial proof of the Jacobi Triple Product and combine with a proof of Hirschhor…

math.CO2019

On $q$ -analogues Arising from Elliptic Integrals and the Arithmetic-Geometric Mean

Mario DeFranco

We prove $q$ -analogues of identities that are equivalent to the functional equation of the arithmetic-geometric mean. We also present $q$ -analogues of $F (k, \frac{π}{2})$ , the…

On properties of the Taylor series coefficients of the Riemann xi function at s=21​

A Constructive Proof of Jacobi's Identity for the Sum of Two Squares

On q-analogues Arising from Elliptic Integrals and the Arithmetic-Geometric Mean

On properties of the Taylor series coefficients of the Riemann xi function at $s = \frac{1}{2}$

On $q$ -analogues Arising from Elliptic Integrals and the Arithmetic-Geometric Mean