Cuspidal groups, ordinary Eisenstein series, and Kubota-Leopoldt \(p\)-adic \(L\)-functions (Q2717585)

Let \(p\) be a fixed prime \(\geq 5\) and \(N> 1\) a squarefree positive integer prime to \(p\). Let \(C_n\) denote the \(p\)-primary part of the cuspidal divisor class group attached to the congruence group \(\Gamma_1(p^nN)\). Let \(C^0_n\) denote the ordinary part of \(C_n\).NEWLINENEWLINE The author proves the following analogue of Stickelberger's theorem. He constructs a canonical ``weight two'' Bernoulli measure \(\beta\) which annihilates \(C^0_n\) for all \(n\geq 1\) (Theorem 5.14). The measure \(\beta\) leads naturally to the construction of an everywhere analytic \(p\)-adic \(L\)-function \(L^*_p(s,\xi)\) (a modification of the Kubota-Leopoldt \(p\)-adic \(L\)-function, cf. Theorem 1.13).NEWLINENEWLINE The results extend some of those of \textit{B. Mazur} and \textit{A. Wiles} [Invent. Math. 76, 179--330 (1984; Zbl 0545.12005)] to the groups \(C^0_n\).