科研之友
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摘要
For non-square 1 < D equivalent to 0, 1 (mod 4), Don Zagier defined a function A(D)(x) by summing over certain integral quadratic polynomials. He proved that A(D)(x) is a constant function depending on D. For rational x, it turns out that this sum has finitely many terms. Here we address the infinitude of the number of quadratic polynomials for non-rational x, and more importantly address some problems posed by Zagier related to characterizing the polynomials which arise in terms of the continued fraction expansion of x. In addition, we study the indivisibility of the constant functions A(D)(x) as D varies.
- 出版日期2016-2
