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Explicit formulae for L-functions
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the <a href="/facts/Closed-form_expression/y0xCXlSk">explicit formulae</a> for <a href="/facts/L-function/REVCKvU7">L-functions</a> are relations between sums over the <a href="/facts/Complex_number/2w7mqI7e">complex number</a> zeroes of an <a href="/facts/L-function/REVCKvU7">L-function</a> and sums over <a href="/facts/Prime_number/L20FLkgn">prime powers</a>, introduced by Riemann (1859) for the <a href="/facts/Riemann_zeta_function/MnfRu7lY">Riemann zeta function</a>. Such explicit formulae have been applied also to questions on bounding the <a href="/facts/Discriminant_of_an_algebraic_number_field/mvv6MWKj">discriminant of an algebraic number field</a>, and the <a href="/facts/Conductor_of_a_number_field/KFN786uM">conductor of a number field</a>. </p>