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Multiplicative functions dictated by Artin symbols

Robert J. Lemke Oliver (2013)

Acta Arithmetica

Granville and Soundararajan have recently suggested that a general study of multiplicative functions could form the basis of analytic number theory without zeros of L-functions; this is the so-called pretentious view of analytic number theory. Here we study multiplicative functions which arise from the arithmetic of number fields. For each finite Galois extension K/ℚ, we construct a natural class K of completely multiplicative functions whose values are dictated by Artin symbols, and we show that...

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 .

Currently displaying 161 – 180 of 367