Revision as of 16:19, 11 January 2009 edit Michael Hardy (talk \| contribs) Administrators 210,577 edits →Explicit formula for the Riemann zeta function: math notation edits ← Previous edit		Revision as of 16:19, 11 January 2009 edit undo Michael Hardy (talk \| contribs) Administrators 210,577 edits →Explicit formula for the Riemann zeta function: minus Next edit →
Line 20: :: <math>\varphi(t) = \int_{-\infty}^\infty F(x)e^{itx}\,dx</math> Φ(1/2 + ''it'') = ''φ''(''t'') ''Ψ''(''t'') = -−log(''π'') + Re(''ψ''(1/4 + ''it''/2)), where ''ψ'' is the [[digamma function]] Γ′/Γ. Roughly speaking, the explicit formula says the Fourier transform of the zeros of the zeta function is the set of prime powers plus some elementary factors.

Explicit formulae for L-functions: Difference between revisions