On linear relations for L-values over real quadratic fields

2017/11/01 by Su, Ren-He
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1711.00293

Abstract

In this paper, we give a method to construct a classical modular form from a Hilbert modular form. By applying this method, we can get linear formulas which relate the Fourier coefficients of the Hilbert and classical modular forms. The paper focuses on the Hilbert modular forms over real quadratic fields. We will state a construction of relations between the special values of L-functions, especially at 0, and arithmetic functions. We will also give a relation between the sum of squares functions with underlying fields ℚ(√(D)) and ℚ.

Related

• Notes on the arithmetic of Hilbert modular forms
• Kernels for products of Hilbert L-functions
• Central values of L-functions over CM fields
• Determination of Hilbert modular forms using squarefree coefficients
• Twisted Hilbert modular L-functions and spectral theory