an:06723336
Zbl 1379.57041
Guo, Victor J. W.; Han, Fei
On certain multi-variable rational identities derived from the rigidity of signature of manifolds
EN
J. Math. Anal. Appl. 453, No. 1, 360-365 (2017).
00366061
2017
j
57S15 58J26 58J20 11F27 05A19
signature; rigidity; fixed point theorem; \(q\)-Lucas theorem; theta function; identities
Summary: \textit{R. Song} [Sci. China, Ser. A 48, No. 12, 1637--1645 (2005; Zbl 1217.58015)] derives certain multi-variable rational identities by studying torus actions on some homogeneous manifolds and applying the Atiyah-Bott-Segal-Singer Lefschetz fixed point theorem. In this paper, we give a direct proof of these rational identities by using the \(q\)-Lucas theorem. Moreover, we also give a similar new rational identity.
Zbl 1217.58015