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revised What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
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Apr
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comment What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
on the "in some sense": the -1/12 in string theory is related to the fact that the discriminant function $\Delta$ is modular of weigth 12. It is this fact which is directly related to the Euler characteristic of the moduli of elliptic curves by a first Chern class argument.
Mar
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answered What are some geometric / physical / probabilistic interpretations of the Riemann zeta function at integer arguments n ≤ 1?
Mar
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comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
Another point: maybe Gamma factors at the Archimedean places are most easily undestood on the automorphic side of the story. I am certainly not an expert of these questions and I hope someone else will say more.
Mar
29
comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
About the date 1991: from what I understand, the story of the Deninger interpretation is somewhat involved: it is motivated by p-adic Hodge theory and not directly by the usual formulation of Hodge theory.
Mar
29
comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
The only motivation I see in the paper of Serre is that Gamma factors appear in the known examples (number fields, modular curves...) It would be great if someone could say if Serre had more conceptual motivations, I don't know.
Mar
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awarded  Nice Question
Mar
28
revised What is the meaning of $(h^{11},h^{21})\to (h^{11}-240,h^{21}+240)$ in Calabi-Yau threefolds?
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Mar
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comment Hodge Decompositions and Gamma Factors of Hasse--Weil L-Functions
Do you know the work of Deninger "On the \Gamma factors attached to motives", Invent. Math. 104 (1991) 245-261?
Mar
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answered What is the meaning of $(h^{11},h^{21})\to (h^{11}-240,h^{21}+240)$ in Calabi-Yau threefolds?
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answered SU(2) Lefschetz decomposition for cohomology of Riemann surface Jacobian
Nov
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comment Moduli space of motives vs moduli space of varieties
If I want that my preceding comment makes sense, I should rather say : such that the family of Hodge structures over C admits a connection such that Griffits transversality is satisfied (i.e. one has a "variation of Hodge structures")
Nov
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comment Moduli space of motives vs moduli space of varieties
related : mathoverflow.net/questions/114847/…
Nov
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comment Moduli space of motives vs moduli space of varieties
Let H in D be in the "image of motives". Let C a germ of curve in D through H such that the family of Hodge structures over C satisfies Griffits transversality. Is C in the "image of motives"? (In other words, is Griffiths transversality the only obstruction)