Automorphic form
Automorphic form In mathematics, the general notion of automorphic form is the extension to analytic functions, perhaps ... corresponding to the possibility of vector-valued automorphic forms. The cocycle condition imposed on ...
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Talk:Automorphic form
Talk:Automorphic form Condition 2 isn't quite right, it ...
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Modular form
Modular form In mathematics, a modular form is a (complex) analytic function on the ... as algebraic topology and string theory. Modular form theory is a special case of the more general theory of automorphic forms, and therefore can now be seen ... end of the nineteenth century, as the automorphic form concept was understood (for one ...
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Automorphic number
Automorphic number In mathematics an automorphic number is a number whose square "ends ... 2 = 5776, and 890625 2 = 793212890625. The automorphic numbers begin 1, 5, 6, 25, 76 ... A003226 in OEIS) Given a k-digit automorphic number $n>1$, an at-most 2k-digit automorphic number $n\text{'}$ can be ...
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Cusp form
Cusp form In number theory, a cusp form is a particular kind of modular form, distinguished in the case of modular forms ... definition amounts to saying that a cusp form is a modular form that vanishes at a cusp. In ...
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Modular form   (translated from French)
Modular form In mathematic , one modular form is one analytical function on demi-plan ... networks At the simplest level, a modular form can be thought like a function F ... generally a positive entirety) called it weight form. (3) the absolute value of F ... degrees K. On a side, this one form a vector space of size finished ...
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Category:Automorphic forms
Category:Automorphic forms Subcategories There are 2 subcategories to ... functions M Modular forms Pages in category "Automorphic forms" There are 6 pages in this section of this category. * Automorphic form H Hilbert modular form Hilbert's twenty-second problem K ...
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List of mathematics articles (A-C)
... Algebraic element -- Algebraic enumeration -- Algebraic extension -- Algebraic form -- Algebraic function -- Algebraic geometry -- Algebraic geometry and ... Algebraic integer -- Algebraic K-theory -- Algebraic normal form -- Algebraic number -- Algebraic number field -- Algebraic number ... Automatic differentiation -- Automatic group -- Automatic label placement -- Automorphic form -- Automorphic number -- Automorphism -- Automorphism group -- Autonomous category -- ...
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Langlands program
... way: Artin L-functions. The setting of automorphic representations The insight of Langlands was to ... had earlier related Dirichlet L-functions with automorphic forms (holomorphic functions on the upper half ... functional equations). Langlands then generalized these to automorphic cuspidal representations, which are certain infinite dimensional ... numbers.) Langlands attached L-functions to these automorphic representations, and conjectured that every Artin L ... is equal to one arising from an automorphic cuspidal representation. This is known as ...
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Eisenstein series
... can be generalized in the theory of automorphic forms. Eisenstein series for the modular group ... that the Eisenstein series is a modular form. Explicitly if $a,b,c,d\; ...\; G\_\{2k\}$ is therefore a modular form of weight $2k$. Relation to ... theta functions. Recurrence relation Any holomorphic modular form for the modular group can be written ... Grutyer and Co. (1998), 371-382. Generalizations Automorphic forms generalize the idea of modular ...
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