Bernoulli and poly-Bernoulli polynomial convolutions and identities of \(p\)-adic Arakawa-Kaneko zeta functions (Q2810675)

The author obtains an explicit expression for the convolution \(\sum\limits_{j=0}^n B_j(a)B_{n-j}(a)\) of the Bernoulli polynomials via the poly-Bernoulli polynomials [\textit{M. Kaneko}, J. Theor. Nombres Bordx. 9, No. 1, 221--228 (1997; Zbl 0887.11011)]. This identity is then interpreted as a relation for \(p\)-adic Arakawa-Kaneko zeta functions, which interpolate the poly-Bernoulli polynomials at negative integers and whose values at positive integers are related to multiple zeta values and series of generalized harmonic numbers; see [the author, J. Number Theory 155, 13--35 (2015; Zbl 1320.11086)].