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The linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$

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arxiv 2408.15403 v2 pith:2HFA2YAO submitted 2024-08-27 math.NT

Frank Calegari , Vesselin Dimitrov , Yunqing Tang This is my paper · ORCID
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keywords independenceirrationalitylinearotherzetaapplicationsappliesargument
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abstract

We prove the irrationality of the classical Dirichlet L-value $L(2,\chi_{-3})$. The argument applies a new kind of arithmetic holonomy bound to a well-known construction of Zagier. In fact our work also establishes the $\mathbf{Q}$-linear independence of $1$, $\zeta(2)$, and $L(2,\chi_{-3})$. We also give a number of other applications of our method to other problems in irrationality.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. On Conservative Matrix Fields: Continuous Asymptotics and Arithmetic

    math.NT 2025-07 conditional novelty 6.0 of 10

    Conservative Matrix Fields generalize Apéry-type ratios of D-finite sequences to several dimensions and conjecturally have direction-continuous convergence and irrationality measures.

  2. G-functions, motives, and unlikely intersections -- old and new

    math.NT 2025-01 unverdicted novelty 1.0 of 10

    A survey of the G-function method, its link to periods, and its use in proving cases of unlikely intersection conjectures.

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