A spectral interpretation for the explicit formula in the theory of prime numbers

作者：Li Xian Jin^*

来源：Science China Mathematics, 2010, 53(3): 791-812.

DOI：10.1007/s11425-009-0215-3

• explicit formula
• fourier analysis
• Riemann hypothesis
• trace formula

A spectral interpretation for the poles and zeros of the L-function of algebraic number fields is given by Meyer. As Meyer works with Schwartz spaces which are not Hilbert spaces, the information on the location of zeros of the L-function is lost. In 1999, A. Connes gave a spectral interpretation for the critical zeros the Riemann zeta function. He works with Hilbert spaces. In this paper, we show that a variant of Connes' trace formula is essentially equal to the explicit formula of A. Weil.

• 出版日期2010-3