The logarithmic derivative of the -function, namely the -function, has numerous applications. We define analogous functions in a four dimensional space. We cut lattices and obtain Clifford-valued functions. These functions are holomorphic cliffordian and have similar properties as the -function. These new functions show links between well-known constants: the Euler gamma constant and some generalisations, , . We get also the Riemann zeta function and the Epstein zeta functions.
Cite this article
Guy Laville, Louis Randriamihamison, Logarithmic derivative of the Euler -function in Clifford analysis. Rev. Mat. Iberoam. 21 (2005), no. 3, pp. 695–728DOI 10.4171/RMI/433