- Title
- Higher Hickerson formula
- Authors
- Lee J.; Jun B.; Chae H.-J.
- Ewha Authors
- 이정연
- SCOPUS Author ID
- 이정연
- Issue Date
- 2017
- Journal Title
- Journal of Number Theory
- ISSN
- 0022-314X
- Citation
- Journal of Number Theory vol. 170, pp. 191 - 210
- Keywords
- Generalized Dedekind sums; Meyer's formula; Partial zeta function; Real quadratic fields; Siegel's formula
- Publisher
- Academic Press Inc.
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- In [11], Hickerson made an explicit formula for Dedekind sums s(p,q) in terms of the continued fraction of p/q. We develop analogous formula for generalized Dedekind sums si,j(p,q) defined in association with the xiyj-coefficient of the Todd power series of the lattice cone in R2 generated by (1,0) and (p,q). The formula generalizes Hickerson's original one and reduces to Hickerson's for i=j=1. In the formula, generalized Dedekind sums are divided into two parts: the integral sij I(p,q) and the fractional sij R(p,q). We apply the formula to Siegel's formula for partial zeta values at a negative integer and obtain a new expression which involves only sij I(p,q) the integral part of generalized Dedekind sums. This formula directly generalizes Meyer's formula for the special value at 0. Using our formula, we present the table of the partial zeta value at s=−1 and −2 in more explicit form. Finally, we present another application on the equidistribution property of the fractional parts of the graph (pq,Ri+jqi+j−2sij(p,q)) for a certain integer Ri+j depending on i+j. © 2016 Elsevier Inc.
- DOI
- 10.1016/j.jnt.2016.06.003
- Appears in Collections:
- 연구기관 > 수리과학연구소 > Journal papers
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