bio  website  

location  
age  
visits  member for  3 years, 11 months 
seen  19 mins ago  
stats  profile views  10,324 
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
edited tags 
2d

awarded  Nice Answer 
2d

awarded  referencerequest 
2d

comment 
Tate's thesis for Artin Lfunctions
@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. 
2d

comment 
Tate's thesis for Artin Lfunctions
@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 Lfunctions
@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 Lfunctions
@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 Lfunctions 
Dec 23 
awarded  Nice Answer 
Dec 23 
revised 
Growth of $r_{2}(n)$
edited body 
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 $r_{2}(n)$
added 19 characters in body 
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
added 8 characters in body 
Dec 20 
answered  Real algebraic solution 
Dec 16 
comment 
Finding integer points on elliptic curves via divisibility conditions like $(a+b)^2 \mid (2b^3+6ab^21)$
@KierenMacMillan: Mail sent! 
Dec 16 
revised 
Zeros of the derivative of Riemann's $\xi$function
edited tags 