An arithmetic formula for certain coefficients of the Euler product of Hecke polynomials
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 Lfunctions attached to weight 2 cusp forms (both newforms and oldforms) over Hecke congruence subgroups. The nonnegativity of these coefficients gives a criterion for the Riemann hypothesis for all these Lfunctions at once.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 March 2004
 arXiv:
 arXiv:math/0403148
 Bibcode:
 2004math......3148L
 Keywords:

 Mathematics  Number Theory;
 11M26;
 11M36