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-function, ''L''-func ...
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. ...
affects the location of the zeros of other Dirichlet L-functions.
See also
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Siegel zero
Siegel (also Segal or Segel), is a German and Ashkenazi Jewish surname. it can be traced to 11th century Bavaria and was used by people who made wax seals for or sealed official documents (each such male being described as a ''Siegelbeamter''). ...
References
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{{DEFAULTSORT:Deuring-Heilbronn phenomenon
Analytic number theory