ON THE VALUE DISTRIBUTION OF TWO DIRICHLET L-FUNCTIONS

• Let rho denote the non-trivial zeros of the Riemann zeta function. We study the relative value distribution of L(rho + sigma, chi(1)) and L(rho + sigma, chi(2)), where sigma is an element of[0, 1/2) is fixed and chi(1), chi(2) are two fixed Dirichlet characters to distinct prime moduli. For sigma > 0 we prove that a positive proportion of these pairs of values are linearly independent over R, which implies that the arguments of the values are different. For sigma = 0 we show that, up to height T, the values are different for cT of the Riemann zeros for some positive constant c.

Ämnesord

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Nyckelord

Dirichlet L-function

value-distribution

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