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math.NT2007
A note on a curious formula for Euler's constant
Mathew D. Rogers
In this short note we will use the residue theorem to establish a formula for Euler's constant. In particular, we offer a slightly generalized version of an interesting infinite se…
math.NT2007
An extension of Boyd's -adic algorithm for the harmonic series
Mathew D. Rogers
In this paper we will extend a -adic algorithm of Boyd in order to study the size of the set: \[J_p(y)=\left\{n :\sum_{j=1}^{n}\frac{y^j}{j}\equiv 0(\mod p)\right\}.\] Suppose t…
math.NT2007
New hypergeometric transformations, three-variable Mahler measures, and formulas for
Mathew D. Rogers
New relations are established between families of three-variable Mahler measures. Those identities are then expressed as transformations for the hypergeometric function. We…