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Dedekind sums in finite characteristic. (English) Zbl 1225.11055

Summary: This paper is concerned with Dedekind sums in finite characteristic. We introduce Dedekind sums for lattices, and establish the reciprocity law for them.

MSC:

11F20 Dedekind eta function, Dedekind sums
11F52 Modular forms associated to Drinfel’d modules
11G09 Drinfel’d modules; higher-dimensional motives, etc.
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References:

[1] D. Goss, The algebraist’s upper half-plane, Bull. Amer. Math. Soc. (N.S.) 2 (1980), no. 3, 391-415. · Zbl 0433.14017 · doi:10.1090/S0273-0979-1980-14751-5
[2] Y. Hamahata, Dedekind sums for finite fields, In: Diophantine Analysis and Related Fields: DARF 2007/2008. AIP Conference Proceedings , American Institute of Physics, (2008), 976 , pp. 96-102.
[3] S. Okada, Analogies of Dedekind sums in function fields, Mem. Gifu Teach. Coll., 24 , (1989) 11-16.
[4] R. Sczech, Dedekindsummen mit elliptischen Funktionen, Invent. Math. 76 (1984), no. 3, 523-551. · Zbl 0521.10021 · doi:10.1007/BF01388472
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