Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6415424 | Journal of Number Theory | 2015 | 20 Pages |
Abstract
We study certain real functions defined in a very simple way by Zagier as sums of powers of quadratic polynomials with integer coefficients. These functions give the even parts of the period polynomials of the modular forms which are the coefficients in the Fourier expansion of the kernel function for the Shimura-Shintani correspondence. We give three different representations of these sums in terms of a finite set of polynomials coming from reduction of binary quadratic forms and in terms of the infinite set of transformations occurring in a continued fraction algorithm of the real variable. We deduce the exponential convergence of the sums, which was conjectured by Zagier as well as one of the three representations.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Paloma Bengoechea,