Bohr–Courant theorem

E904000

mathematical theorem theorem in analytic number theory

The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.

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Label	Occurrences
Bohr–Courant theorem canonical	1

Statements (28)

Predicate	Object
instanceOf	mathematical theorem ⓘ theorem in analytic number theory ⓘ
appliesTo	Dirichlet series NERFINISHED ⓘ Riemann zeta function NERFINISHED ⓘ
concerns	distribution of values of the Riemann zeta function ⓘ values taken by Dirichlet series in the complex plane ⓘ
describes	value distribution of Dirichlet series ⓘ value distribution of the Riemann zeta function ⓘ
era	early 20th century mathematics ⓘ
field	analytic number theory ⓘ complex analysis ⓘ
hasAuthor	Harald Bohr NERFINISHED ⓘ Richard Courant NERFINISHED ⓘ
historicalRole	early result on value distribution of zeta and L-functions ⓘ precursor to modern universality results in analytic number theory ⓘ
isPrecursorOf	Voronin universality theorem NERFINISHED ⓘ universality theorems for the Riemann zeta function ⓘ
isRelatedTo	Bohr–Jessen theory NERFINISHED ⓘ Bohr’s work on almost periodic functions ⓘ universality theorems ⓘ value-distribution of holomorphic functions ⓘ
namedAfter	Harald Bohr NERFINISHED ⓘ Richard Courant NERFINISHED ⓘ
topic	Dirichlet series ⓘ Riemann zeta function NERFINISHED ⓘ value-distribution theory of zeta-functions ⓘ
usedIn	research on universality of zeta and L-functions ⓘ studies of complex zeros and values of Dirichlet series ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

Voronin universality theorem → relatedTo → Bohr–Courant theorem ⓘ