In mathematics, the Deuring–Heilbronn phenomenon, discovered by and , states that a counterexample to the
generalized Riemann hypothesis
The Riemann hypothesis is one of the most important conjectures in mathematics. It is a statement about the zeros of the Riemann zeta function. Various geometrical and arithmetical objects can be described by so-called global ''L''-functions, whi ...
for one
Dirichlet L-function
In mathematics, a Dirichlet L-series is a function of the form
:L(s,\chi) = \sum_^\infty \frac.
where \chi is a Dirichlet character and s a complex variable with real part greater than 1 . It is a special case of a Dirichlet series. By anal ...
affects the location of the zeros of other Dirichlet L-functions.
See also
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Siegel zero
In mathematics, more specifically in the field of analytic number theory, a Landau–Siegel zero or simply Siegel zero, also known as exceptional zeroSee Iwaniec (2006).), named after Edmund Landau and Carl Ludwig Siegel, is a type of potential cou ...
References
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{{DEFAULTSORT:Deuring-Heilbronn phenomenon
Analytic number theory