Geodesic
p-Adic Eigen-Eunctions for Kubert Distributions
Canadian journal of mathematics, Tome 35 (1983) no. 4, pp. 674-686

Voir la notice de l'article provenant de la source Cambridge University Press

Functions on R (or on R/Z, or Q/Z, or the interval (0,1)) which satisfy the identity 1.1 for positive integers m and fixed complex s, appear in several branches of mathematics (see [8], p. 65-68). They have recently been studied systematically by Kubert [6] and Milnor [12]. Milnor showed that for each complex s there is a one-dimensional space of even functions and a one-dimensional space of odd functions which satisfy (1.1). These functions can be expressed in terms of either the Hurwitz partial zeta-function or the polylogarithm functions.My purpose is to prove an analogous theorem for p-adic functions. The p-adic analog is slightly more general; it allows for a Dirichlet character χ 0(m) in front of m s–l in (1.1). The functions satisfying (1.1) turn out to be p-adic “partial Dirichlet L-functions”, functions of two p-adic variables (x, s) and one character variable χ 0 which specialize to partial zeta-functions when χ 0 is trivial and to Kubota-Leopoldt L-functions when x = 0. 
Koblitz, Neal. p-Adic Eigen-Eunctions for Kubert Distributions. Canadian journal of mathematics, Tome 35 (1983) no. 4, pp. 674-686. doi: 10.4153/CJM-1983-038-8
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