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English is not my native tongue. German is not my native tongue. French is not my native tongue.


10h
revised Algorithm Involving Quadratic Diophantine Equation
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awarded  Nice Answer
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awarded  reference-request
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comment Tate's thesis for Artin L-functions
@Myshkin: I am not familiar with Fesenko's work. Of course you don't need to know beforehand that the underlying object is automorphic. It is possible that Artin's conjecture will be proven without automorphic forms. At any rate, it seems your original question is too vague.
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comment Tate's thesis for Artin L-functions
@Myshkin: A Galois representation is a global object, just as an automorphic form. But we don't know how to define the $L$-function as directly in terms of a Galois representation as in terms of an automorphic form. So the analytic properties of an Artin $L$-function are much less accessible than those of automorphic $L$-functions. Tate's thesis is completely analytic, it lives on the automorphic side.
Dec
23
comment Tate's thesis for Artin L-functions
@Myshkin: Very vaguely, the $L$-function of an automorphic form can be defined rather directly, via an integral (or a family of integrals). The $L$-function of a Galois representation is defined indirectly, in terms of local data. The fact that the latter local data gives rise to a nice global object (with analytic continuation to $\mathbb{C}$ and functional equation) is far less obvious than in the case of automorphic $L$-functions. So much less obvious that we only conjecture these properties for Artin $L$-functions.
Dec
23
comment Tate's thesis for Artin L-functions
@Myshkin: Once again, Tate's thesis is not about Artin $L$-functions. There is no Galois representation in his thesis. Instead, he works with idele class group characters, i.e. very special automorphic forms. It was generalized to more general automorphic forms, that is all.
Dec
23
answered Tate's thesis for Artin L-functions
Dec
23
awarded  Nice Answer
Dec
23
revised Growth of $r_{2}(n)$
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Dec
23
comment Growth of $r_{2}(n)$
I edited your last two lines to make it more precise (and valid).
Dec
23
revised Growth of $r_{2}(n)$
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Dec
23
revised Growth of $r_{2}(n)$
added 10 characters in body
Dec
23
answered Growth of $r_{2}(n)$
Dec
20
accepted $\zeta(0)$ and the cotangent function
Dec
20
comment What happens to the angles of an isosceles triangle if one vertex is at infinity?
In Euclidean geometry, the angles of a triangle are positive and sum up to 180 degrees. In particular, the base angles of an isosceles triangle are less than 90 degrees. You can introduce generalized triangles with a "vertex at infinity", but this is not standard terminology. At any rate, this site is for research level questions. For general questions in mathematics try math.stackexchange.com
Dec
20
revised Real algebraic solution
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Dec
20
answered Real algebraic solution
Dec
16
comment Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^2-1)$
@KierenMacMillan: Mail sent!
Dec
16
revised Zeros of the derivative of Riemann's $\xi$-function
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