Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9496519 | Journal of Number Theory | 2005 | 26 Pages |
Abstract
In 1997 the author found a criterion for the Riemann hypothesis for the Riemann zeta function, involving the nonnegativity of certain coefficients associated with the Riemann zeta function. In 1999 Bombieri and Lagarias obtained an arithmetic formula for these coefficients using the “explicit formula” of prime number theory. In this paper, the author obtains an arithmetic formula for corresponding coefficients associated with the Euler product of Hecke polynomials, which is essentially a product of L-functions attached to weight 2 cusp forms (both newforms and oldforms) over Hecke congruence subgroups Î0(N). The nonnegativity of these coefficients gives a criterion for the Riemann hypothesis for all these L-functions at once.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Xian-Jin Li,