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Non-vanishing of class group L -functions at the central point

Valentin Blomer (2004)

Annales de l’institut Fourier

Let K = ( - D ) be an imaginary quadratic field, and denote by h its class number. It is shown that there is an absolute constant c > 0 such that for sufficiently large D at least c · h p D ( 1 - p - 1 ) of the h distinct L -functions L K ( s , χ ) do not vanish at the central point s = 1 / 2 .

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