Mario DeFranco

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20182021

ζ ({2}^{k})

1 citations · 1 across the 8 of their papers we have counts for

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math.NT2019

On the Bernoulli Numbers via the Newton-Girard Identities

Mario DeFranco

We prove formulas for the Bernoulli numbers by using the Newton-Girard identities to evaluate the Riemann zeta function at positive even integers. To do this, we define a sequence…

math.NT2019★ 1 cited

On the Multiple Zeta Values $ζ ({2}^{k})$

Mario DeFranco

We evaluate the multiple zeta values $ζ ({2}^{k})$ by proving a certain factorization property. The proof uses a combinatorial bijection and elementary telescoping series. We show h…

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…

On the Bernoulli Numbers via the Newton-Girard Identities

On the Multiple Zeta Values ζ({2}k)

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

On the Multiple Zeta Values $ζ ({2}^{k})$

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