Explicit formulae for L-functions: Difference between revisions

Revision as of 21:45, 8 January 2009

Revision as of 21:47, 8 January 2009

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In [[mathematics]], the '''explicit formulae for [[L-function]]s''' relateare relations between sums taken over the complex number zeroes of a givenan L-function toand sums over prime powers. The first case, wasintroduced found by {{harvtxt|Riemann|1959}} for the [[Riemann zeta function]], where sums over its complex zeroes are identified with other sums over [[prime number]]s. Such explicit formulae have been applied also to questions on bounding the [[discriminant of an algebraic number field]], and the [[conductor of a number field]].

==Explicit formula for the Riemann zeta function==