About the Cover: Zeta-functions Associated with Quadratic Forms in Adolf Hurwitz’s Estate

The first published proof of key analytic properties of zeta-functions associated with quadratic forms is due to Paul Epstein [2] in 1903 (submitted January 1902). The corresponding name “Epstein zeta-functions” was introduced by Edward Charles Titchmarsh in his article [15] from 1934; soon after, this terminology became common through influential articles of Max Deuring and Carl Ludwig Siegel. While examining Adolf Hurwitz’s mathematical estate at ETH Zurich, however, the authors discovered that Hurwitz could have published these results already during his time in Königsberg (now Kaliningrad) in the late 1880s. Unpublished notes of Hurwitz testify that he was not only aware of the analytic properties of zeta-functions associated with quadratic forms but prepared a fair copy of his notes, probably for submission to a journal. The cover of this issue shows the first page (see Figure 1). Given a quadratic form φ(x1, x2, . . . , xp) = ∑p i,k=1 aikxixk and real parameters u1, u2, . . . , up; v1, v2, . . . , vp, Hurwitz considers the associated Dirichlet series