Pure and Applied Mathematics Quarterly

Volume 19 (2023)

Number 4

Special Issue in honor of Victor Guillemin

Guest Editors: Yael Karshon, Richard Melrose, Gunther Uhlmann, and Alejandro Uribe

Dedekind sums via Atiyah–Bott–Lefschetz

Pages: 1799 – 1802

DOI: https://dx.doi.org/10.4310/PAMQ.2023.v19.n4.a3


Ana Cannas da Silva (Department of Mathematics, ETH Zurich, Switzerland)


This paper, written for differential geometers, shows how to deduce the reciprocity laws of Dedekind and Rademacher, as well as $n$-dimensional generalizations of these, from the Atiyah–Bott–Lefschetz formula, by applying this formula to appropriate elliptic complexes on weighted projective spaces.


global analysis, elementary number theory

2010 Mathematics Subject Classification

11Axx, 58-xx

Received 26 January 2022

Received revised 8 January 2023

Accepted 19 February 2023

Published 20 November 2023