Arithmetic of generalized Dedekind sums and their modularity
AbstractDedekind sums were introduced by Dedekind to study the transformation properties of Dedekind η function under the action of SL2(ℤ). In this paper, we study properties of generalized Dedekind sums si,j(p, q). We prove an asymptotic expansion of a function on ℚ defined in terms of generalized Dedekind sums by using its modular property. We also prove an equidistribution property of generalized Dedekind sums.
2011 ◽
Vol 9
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pp. 529-542
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2005 ◽
Vol 3
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pp. 285-296
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2013 ◽
Vol 72
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pp. 447-460
1985 ◽
Vol 50
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pp. 2697-2714