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Geometry and Analysis of Shimizu L-Functions

M. F. Atiyah, H. Donnelly and I. M. Singer
Proceedings of the National Academy of Sciences of the United States of America
Vol. 79, No. 18, [Part 2: Physical Sciences] (Sep. 15, 1982), p. 5751
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The values at 0 of Shimizu L-functions are realized as the signature defects of framed manifolds. This settles a conjecture of Hirzebruch [Hirzebruch, F. (1973) Enseign. Math. 19, 183-281] affirmatively. The proof employs the spectral theory of elliptic operators.

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