A new integral–series identity of multiple zeta values and regularizations

• Masanobu Kaneko ^[1] ; Shuji Yamamoto ^[2]
  1. [1] Kyushu University

     Kyushu University

     Hakata Ku, Japón

     
  2. [2] Keio University

     Keio University

     Japón

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 24, Nº. 3, 2018, págs. 2499-2521
• Idioma: inglés
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• Resumen

  • We present a new “integral = series” type identity of multiple zeta values, and show that this is equivalent in a suitable sense to the fundamental theorem of regularization. We conjecture that this identity is enough to describe all linear relations of multiple zeta values over Q. We also establish the regularization theorem for multiple zeta-star values, which too is equivalent to our new identity. A connection to Kawashima’s relation is discussed as well.