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The Eisenstein family for the modular group along closed geodesics. (English) Zbl 0868.11023

R. W. Bruggeman [Math. Z. 202, 181-198 (1989; Zbl 0671.10022)] developed distribution results for classical Dedekind sums arising in the transformation formula of the logarithm of the Dedekind \(\eta\)-function. This paper obtains similar results for a class of objects analogous to Dedekind sums associated with the functions in the title.

MSC:

11F20 Dedekind eta function, Dedekind sums
11F11 Holomorphic modular forms of integral weight
30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)

Citations:

Zbl 0671.10022
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References:

[1] Bruggeman, R.W.: Fourier coefficients of modular forms. Lect. Notes in Math.865, Springer-Verlag 1981 · Zbl 0455.10014
[2] Bruggeman, R.W.: Modular forms of varying weight I. Math. Z.190, 477–495 (1985) · Zbl 0553.10021 · doi:10.1007/BF01214747
[3] Bruggeman, R.W.: Modular forms of varying weight II. Math. Z.192, 297–328 (1986) · Zbl 0569.10011 · doi:10.1007/BF01179430
[4] Bruggeman, R.W.: Modular forms of varying weight III. J. Reine Angew. Math.371, 144–190 (1986) · Zbl 0588.10021
[5] Bruggeman, R.W.: Eisenstein series and the distribution of Dedekind sums. Math. Z.202, 181–198 (1989) · Zbl 0655.10026 · doi:10.1007/BF01215253
[6] Bruggeman, R.W.: Dedekind sums for Hecke groups. preprint, Utrecht 1992
[7] Gradshteyn, I.S., Ryzhik, I.M.: Table of integrals, series, products. Academic Press 1980 · Zbl 0521.33001
[8] Lang, S.: Introduction to Modular Forms. Springer-Verlag 1976 · Zbl 0344.10011
[9] Magnus, W., Oberhettinger, F., Soni, R.P.: Formulas and theorems for the special functions of mathematical physics. 3. ed., Springer-Verlag 1966 · Zbl 0143.08502
[10] Neukirch, J.: Algebraische Zahlentheorie. Springer-Verlag 1992 · Zbl 0747.11001
[11] Petersson, H.: Modulfunktionen und quadratische Formen. Springer-Verlag 1982 · Zbl 0493.10033
[12] Rankin, R.A.: Modular Forms and Functions. Cambridge University Press 1977 · Zbl 0376.10020
[13] Zagier, D.: Zetafunktionen und quadratische Körper. Springer-Verlag 1981 · Zbl 0459.10001
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