Dirichlet L-Functions

Part of the Progress in Mathematics book series (PM, volume 157)


Let x denote a Dirichlet character and L(s, x) the associated Dirichlet L-function. Let us begin by considering how one would approach the problem of showing that L(1/2, x) ≠ 0. In the following, we assume that x is defined modulo a prime q. We first study the average
$$ \sum\limits_{{X\left( {\bmod q} \right)}} {L\left( {\frac{1}{2},x} \right).} $$


Main Term Riemann Hypothesis Dirichlet Character Real Character Positive Proportion 
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Copyright information

© Springer Basel AG 1997

Authors and Affiliations

  1. 1.Department of MathematicsQueen’s UniversityKingstonCanada
  2. 2.Department of MathematicsUniversity of TorontoTorontoCanada

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