A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity
Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 1, p. 93-101

In the transformation formulas for the logarithms of the classical theta-functions, certain sums arise that are analogous to the Dedekind sums in the transformation of the logarithm of the eta-function. A new reciprocity law is established for one of these analogous sums and then applied to prove the law of quadratic reciprocity.

Une loi de réciprocité est établie pour des sommes apparaissant dans les formules de transformations pour les logarithmes des fonctions theta, sommes qui sont les analogues des sommes de Dedekind dans la transformation du logarithme de la fonction eta.

@article{JTNB_2000__12_1_93_0,
     author = {Meyer, Jeffrey L.},
     title = {A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {12},
     number = {1},
     year = {2000},
     pages = {93-101},
     zbl = {1005.11014},
     mrnumber = {1827841},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2000__12_1_93_0}
}
Meyer, Jeffrey L. A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity. Journal de théorie des nombres de Bordeaux, Volume 12 (2000) no. 1, pp. 93-101. http://www.numdam.org/item/JTNB_2000__12_1_93_0/

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