TY - JOUR
T1 - Zeros of Dirichlet series
AU - Vaughan, R. C.
N1 - Publisher Copyright:
© 2015 Royal Dutch Mathematical Society (KWG).
PY - 2015/12
Y1 - 2015/12
N2 - We are concerned here with Dirichlet series, which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s)=2sq1/2-sπs-1Γ(1-s)(sinπ/2(s+κ))f(1-s), but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane.
AB - We are concerned here with Dirichlet series, which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s)=2sq1/2-sπs-1Γ(1-s)(sinπ/2(s+κ))f(1-s), but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane.
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U2 - 10.1016/j.indag.2015.09.007
DO - 10.1016/j.indag.2015.09.007
M3 - Article
AN - SCOPUS:84947587860
SN - 0019-3577
VL - 26
SP - 897
EP - 909
JO - Indagationes Mathematicae
JF - Indagationes Mathematicae
IS - 5
ER -