Journal of the Ramanujan Mathematical Society

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Special Relations Between Multizeta Values and Parity Results


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1 Departamento de Control Automatico, Centro de Investigacion y de Estudios Avanzados del IPN, Av. Instituto Politecnico Nacional 2508, San Pedro Zacatenco, 07360, Mexico
     

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We study relations between multizeta values for function fields introduced by Thakur in [25,24]. The 𝔽p-span of Thakur’s multizeta values is an algebra [26]. In particular, the product ζ(a)ζ (b) is a linear combination of multizeta values. In this paper, several of the conjectures formulated in [16,25] for small values or for special families of a about how to write ζ(a)ζ (b) as an 𝔽p-linear combination of multizeta values, are proved. Also, the parity conjecture formulated in [25] is proved.
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  • Special Relations Between Multizeta Values and Parity Results

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Authors

Jose Alejandro Lara Rodriguez
Departamento de Control Automatico, Centro de Investigacion y de Estudios Avanzados del IPN, Av. Instituto Politecnico Nacional 2508, San Pedro Zacatenco, 07360, Mexico

Abstract


We study relations between multizeta values for function fields introduced by Thakur in [25,24]. The 𝔽p-span of Thakur’s multizeta values is an algebra [26]. In particular, the product ζ(a)ζ (b) is a linear combination of multizeta values. In this paper, several of the conjectures formulated in [16,25] for small values or for special families of a about how to write ζ(a)ζ (b) as an 𝔽p-linear combination of multizeta values, are proved. Also, the parity conjecture formulated in [25] is proved.