On interpolated multiple $L$-values
Volume 208 / 2023
Acta Arithmetica 208 (2023), 171-183
MSC: Primary 11M32.
DOI: 10.4064/aa221102-22-3
Published online: 27 April 2023
Abstract
Interpolated multiple zeta values introduced by S. Yamamoto are generalized to two kinds of multiple $L$-values. Their double shuffle structure is established algebraically. Then we give the extended double shuffle relation, Hoffman’s relation, and Kawashima’s relation for our interpolated multiple $L$-values. We also show that interpolated alternating multiple harmonic sums for any index with the same ‘full-signed’ even arguments lined up are powers of $\pi ^2$ with coefficients in $\mathbb Q[t]$.
