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...oth of the [[prime number theorem]] and of [[Dirichlet's theorem on primes in arithmetic progressions]]. Then the theorem states that given any [[real number]] ''N'' there exists a positive constant ''C''_''N'' depending on ...

{{Short description|Mathematical theorem about the real analytic Eisenstein series}} ...1 of a [[real analytic Eisenstein series]] (or [[Epstein zeta function]]) in terms of the [[Dedekind eta function]]. There are many generalizations of i ...

...tions|Hartogs's extension theorem|the theorem on infinite ordinals|Hartogs number||}} ...{\textbf{C}}</math> is a function which is [[analytic function|analytic]] in each variable ''z''_''i'', 1 &le; ''i'' &le; ''n'', while the oth ...

...rovides an asymptotic formula for counting the number of prime ideals of a number field}} ...des an asymptotic formula for counting the number of [[prime ideal]]s of a number field ''K'', with [[field norm|norm]] at most ''X''. ...

In [[mathematics]], a '''pro-''p'' group''' (for some [[prime number]] ''p'') is a [[profinite group]] <math>G</math> such that for any [[open s ...>\mathbb{Q}_p</math> such that group multiplication and inversion are both analytic functions. ...

...alysis''' is the practice of looking at a problem relative to each [[prime number]] ''p'' first, and then later trying to integrate the information gained at ==Group theory== ...

...|Formula to calculate the sum of an arithmetic function in analytic number theory}} In [[mathematics]], and more particularly in [[analytic number theory]], '''Perron's formula''' is a formula due to [[Oskar Perron]] to calculate ...

...xample of a ''C''¹ diffeomorphism with an irrational [[rotation number]] that is not conjugate to a rotation. ...m of the circle whose rotation number ''θ'' = ''ρ''(''ƒ'') is [[irrational number|irrational]]. Assume that it has positive derivative ''ƒ''{{prime}}(''x'')& ...

This page is a list of articles related to [[set theory]]. ==Articles on individual set theory topics== ...

...atics, including [[number theory]] and [[applied mathematics]]; as well as in [[physics]], including [[hydrodynamics]], [[thermodynamics]], and [[electri * [[Residue theory]] ...

In [[additive combinatorics]], the '''sumset''' (also called the [[Minkowski a :<math>A + B = \{a+b : a \in A, b \in B\}.</math> ...

==Theorems of which articles are primarily devoted to proving them== ==Articles devoted to theorems of which a (sketch of a) proof is given== ...

...(Russian)</ref> who published on a related topic, the density hypothesis, in 1965. ...ic Number Theory | first=Gérald | last=Tenenbaum | series=Graduate Studies in Mathematics | volume=163 | publisher=American Mathematical Society | year=2 ...

In [[mathematics]], '''Birch's theorem''',<ref>{{cite journal | title=Homogeneous forms of odd degree in a large number of variables ...

{{short description|Several textbooks of number theory}} ...[[Edmund Landau]], and [[Helmut Hasse]]. They all cover elementary number theory, Dirichlet's theorem, quadratic fields and forms, and sometimes more advanc ...

...al results factored out of proofs). See also [[list of axioms]], [[list of theorems]] and [[list of conjectures]]. {{Main category|Lemmas in algebra}} ...

{{short description|Theorems whose content is effectively computable}} ...asserted that some list of [[integer]]s is finite, the question is whether in principle the list could be printed out after a machine computation. ...

...to itself in order that recent changes to this page will also be included in ''related changes''.}} ...c]]. See also the [[list of computability and complexity topics]] for more theory of [[algorithm]]s. ...

{{Short description|Local theory of several complex variables}} ...], and whose [[coefficient]]s of lower degree terms are analytic functions in the remaining variables and zero at ''P''. ...

...[[asymptotic analysis|asymptotic distribution law]] similar to the [[prime number theorem]]. ...section presents some facts from [[hyperbolic geometry]] that are helpful in understanding prime geodesics. ...