Research output: Contribution to journal › Article › peer-review

Journal | Journal of Number Theory |
---|---|

Date | Accepted/In press - 1 Jul 2014 |

Date | E-pub ahead of print (current) - 12 Aug 2014 |

Volume | 147 |

Number of pages | 20 |

Pages (from-to) | 24-43 |

Early online date | 12/08/14 |

Original language | English |

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.

- Binary quadratic forms, Continued fractions, Modular forms, Period polynomials

## Programme Grant-New Frameworks in metric Number Theory

Project: Research project (funded) › Research

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