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Applications to elliptic Apostol-Dedekind-Zagier sums. (Applications aux sommes elliptiques d’Apostol-Dedekind-Zagier.) (French. English summary) Zbl 1099.11025

The known sums of Dedekind, Apostol, and Zagier and their reciprocity laws are obtained as limiting cases of results in the author’s earlier paper [A. Bayad, C. R. Acad. Sci. Paris, Sér. I, 339, No. 7, 457–462 (2004), see Zbl 1099.11023 below]

MSC:

11F50 Jacobi forms
11F20 Dedekind eta function, Dedekind sums
11L03 Trigonometric and exponential sums (general theory)

Citations:

Zbl 1099.11023
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Full Text: DOI

References:

[1] Apostol, T. M., Generalized Dedekind sums and transformation formulae of certain Lambert series, Duke Math. J., 17, 147-157 (1950) · Zbl 0039.03801
[2] Apostol, T. M., Theorems on generalized Dedekind sums, Pacific J. Math., 2, 1-9 (1952) · Zbl 0047.04502
[3] Bayad, A., Sommes elliptiques multiples d’Apostol-Dedekind-Zagier, C. R. Acad. Sci. Paris, Ser. I, 339 (2004) · Zbl 1099.11026
[4] Hirzebruch, F., Topological Methods in Algebraic Geometry (1966), Springer: Springer Berlin · Zbl 0138.42001
[5] Zagier, D., Higher order Dedekind sums, Math. Ann., 202, 149-172 (1973) · Zbl 0237.10025
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