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On interpolated multiple $L$-values

Volume 208 / 2023

Shin-ya Ito, Tatsushi Tanaka, Noriko Wakabayashi Acta Arithmetica 208 (2023), 171-183 MSC: Primary 11M32. DOI: 10.4064/aa221102-22-3 Published online: 27 April 2023


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 $\mathbb Q[t]$.


  • Shin-ya ItoKISTEM Co., Ltd.
    Shiga 520-0047, Japan
  • Tatsushi TanakaDepartment of Mathematics
    Faculty of Science
    Kyoto Sangyo University
    Kyoto 603-8555, Japan
  • Noriko WakabayashiCenter of Physics and Mathematics
    Institute for Liberal Arts and Sciences
    Osaka Electro-Communication University
    Osaka 575-0063, Japan

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