Projects per year
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 ShimuraShintani 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.
Original language  English 

Pages (fromto)  2443 
Number of pages  20 
Journal  Journal of Number Theory 
Volume  147 
Early online date  12 Aug 2014 
DOIs  
Publication status  Epub ahead of print  12 Aug 2014 
Keywords
 Binary quadratic forms
 Continued fractions
 Modular forms
 Period polynomials
Projects
 1 Finished

Programme GrantNew Frameworks in metric Number Theory
1/06/12 → 30/11/18
Project: Research project (funded) › Research