As editor of this inonugjaph oil polvlogarilhins i would like to lake the liberty of commencing wilh a few pergonal utniiibeenees. 1 tnst LiiiuunKKd I he dilogarilhm Junction many years ago m high school; H wai a Li^mating discovery lor me, and и initiated a romance that has lasted almost м.м> u..u.> For the ditogaiithm, the transition from its standing as a mi ишь dliIIkiimh cal oddity to its current status as an important element m the t.ilnk ol modem mathematical structure began about lilievn jeats ago with Hi-. 1Л, studies on its applications in algebraic Л'-lheory and algebiaic gcomeii> Vine then, the pace of discovery has quickened dramatically, in 1УЙ0, wla n I л as ш the throes of completing my "Polylogarithms and Assouaicd I uintiont " I Ijl-cumc dimly aware thui the hundtut ot peculiui numciual tduiuuu> tt„a had been known since the lime of Euler and Landen weie, in tail jusl tlie hpol an iceberg of unlimited extent. Thusemuged the new discovenes on i)cluiomic equations and their related polylogarilhniic "ladder - -a nuiDauLiiim. tl.,u came to me in a dream, alter much chewing ovei ol uihei, ими' ап.п. i,,l, verbal constructs, Jen years of development in this arena, u.mluUal ntustly by the methods of classical analysis with the liclp of nunibei к uncling ошь pulers, ran paiallel with other, and more impoitanl, Jr-nuui.. . ш .Iikisc branches of absliau ulgebia and algebmie geometry. 11k ^-Hiltuuu'ul these two streams of thought in the last few years, due to the v. oil, .,1 ^vu.d nuth-ematicians, but paitkulail) to studies of litowtm m Poland and . .;Lui m Germany, has lead lu Die present synthesis whn.li I liave tued to j,iv.sem in this timely, I hope, monograph.
One of the biggest pioblems has be it the pave of new ..-.v.iuli it is о In i-oubty exlieinely dilhcull to produce a book thai iscuiunl v. 1ки in. л Jimuui-ieb are taking place all the time and making alread> wholh iu.iUii.,1 puiiiully outdated—though it is also a sign of л \vi , tU>uns,Umg lurUl ччiw u it.u^> j>i this way. Outing the approximately lwei\e months that tin U,uk n.ii been in a live piepaiation man> new discoveries were made 1 have emka\uied to ktcp the material up io-daic* by the last minute iiuiu..i. .i >•* i - .ijipeiidkvs: one on a special workshop on polylogarilhnis held in Nm.-niK. v*4u ..nd one on vu) ivtviit disio\ cites uii the relation of futKii- ,. i. .jiuii.hi:, lu poi>-logarilhniic ladders, Dedektnd's /eta function; and u^hMing the icnuikauk. discovery by D. Zagiei and 11. Gungl at tlie Мал-1'lamk-liolitui I'm Mathc-