# A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity

Journal de théorie des nombres de Bordeaux (2000)

- Volume: 12, Issue: 1, page 93-101
- ISSN: 1246-7405

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topMeyer, Jeffrey L.. "A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity." Journal de théorie des nombres de Bordeaux 12.1 (2000): 93-101. <http://eudml.org/doc/248501>.

@article{Meyer2000,

abstract = {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.},

author = {Meyer, Jeffrey L.},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {theta functions; reciprocity law},

language = {eng},

number = {1},

pages = {93-101},

publisher = {Université Bordeaux I},

title = {A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity},

url = {http://eudml.org/doc/248501},

volume = {12},

year = {2000},

}

TY - JOUR

AU - Meyer, Jeffrey L.

TI - A reciprocity congruence for an analogue of the Dedekind sum and quadratic reciprocity

JO - Journal de théorie des nombres de Bordeaux

PY - 2000

PB - Université Bordeaux I

VL - 12

IS - 1

SP - 93

EP - 101

AB - 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.

LA - eng

KW - theta functions; reciprocity law

UR - http://eudml.org/doc/248501

ER -

## References

top- [1] B.C. Berndt, Analytic Eisenstein series, theta-functions, and series relations in the spirit of Ramanujan. J. Reine Angew. Math.303/304 (1978), 332-365. Zbl0384.10011MR514690
- [2] L.A. Goldberg, Transformations of theta-functions and analogues of dedekind sums. Ph.D. thesis, Thesis, University of Illinois, Urbana, 1981.
- [3] H. Rademacher E. Grosswald, Dedekind sums. Carus Math. Monogr., vol. 16, Mathematical Association of America, Washington, D.C., 1972. Zbl0251.10020MR357299
- [4] H. Montgomery I. Niven, H. Zuckerman, An introduction to the theory of numbers. 5th ed., John Wiley and Sons, New York, 1991. Zbl0742.11001MR1083765
- [5] J. Lewittes, Analytic continuation of Eisenstein series. Trans. Amer. Math. Soc.171 (1972), 469-490. Zbl0253.10022MR306148
- [6] J.L. Meyer, Analogues of dedekind sums. Ph.D. thesis, University of Illinois, Urbana, 1997. Zbl0889.11013
- [7] _Properties of certain integer-valued analogues of Dedekind sums. Acta Arithmetica82 (1997), 229-242. Zbl0889.11013MR1482888
- [8] H. Rademacher, Topics in analytic number theory. Springer-Verlag, New York, 1973. Zbl0253.10002MR364103

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