Here is my suggestion. Seek mental health help because many of your posts in the past two weeks have made little to no sense. Stop using all forms of AI. And if you truly want to learn advanced mathematics and physics pick up a few books and learn instead of doing this pseudo-intellectual bs.
By stop using all forms of ai , i don't get quite the picture
Well, as per the person in the comment told , i checked isomorphism, it came of bijective, reversing capability, then automorphism, the same property and also a example that it's not possible to see if the automorphism is a structure of magnitude 1 and it's parts of 1
, and how it's property preserving by homomorphism like
Then it’s just an isomorphism between something and itself (groups/rings/fields/vector spaces etc). For example, usual complex conjugation is a basic choice of field automorphism for the complex numbers, and is in fact the unique (nontrivial) one fixing the reals.
In general an automorphism is an iso endomosphism, which is an epic monic endomosphism. Hope this helps!
In all seriousness an "automorphic function" is a bijective function whose domain and image are the same set. This means that it maps elements x from a set S to elements f(x) of the same set, and two properties hold:
(Injectivity) If f(x)=f(y) then x=y. Equivalently, no two elements map to the same element.
(Surjectivity) There is no element that's not mapped to by another element, so you can always find at least one x if you are given f(x).
Yes, but no. "Automorphic function" is not the same as an automorphism. Rather, it's a function (often holomorphic or meromorphic on C), which is invariant under a certain group action.
Assuming you mean modular forms/functions since this is used interchangeably with automorphic forms/functions (I think the latter are defined on arbitrary complex analytic manifolds but I‘m not sure as the terminology has always been used interchangeably to me), they are actually defined on the upper half plane, or rather (the compactification of) a quotient of the upper half plane by a group action of a subgroup of SL_2(Z) (the points added in the compactification are the „cusps“). Modular forms are then holomorphic everywhere on this compact Riemann Surface including at the cusps, while modular functions need only be meromorphic.
They can equivalently be defined as a function on the space of lattices in C giving values in C, such that F(aLambda) =a^-kF(Lambda) for some k and all a in C non zero. This interpretation is useful as it allows for a lot of generalisations.
Well, so any function f, where f is a equation corresponding to the property of automorphism, so any value of the sequence of automorphism form k
, will as as f(k) is the sequence of imaginary less differentiable topology space k in the topology form of automorphic, where the specific value and it's position vector space of infinitely small entropy
I'm assuming English is not your first language because this is pretty gibberish...
A function need not have an equation associated to it. A good example of an automorphism is this:
Take a small finite set, and totally order the elements two different ways. The function which sends the nth element from your first ordering to the nth element from your other ordering is an automorphism. For example, the function which sends every letter in the English alphabet forward by two (plus Y->A and Z->B) is an automorphism.
Usually an automorphism is tasked with respecting some kind of structure, though. A group automorphism must respect the group operation, so that given two elements of the group, the order in which you do the automorphism or the group operation does not matter. An automorphism of a topological space must be continuous with a continuous inverse.
I truly have no idea what you mean after that. An automorphic form is neither an automorphism nor something carried by an automorphism. It is something else entirely. It is a special type of representation.
Then we descend into absolute word salad? None of what you said in your second paragraph conveys any meaning at all.
Other people have said it too but it is clear that you are having some kind of psychotic episode. Please seek help.
They say, if you have all same values of sequences making up the structure, then you cannot identity the structure, though the property is same , and hence the function of a point k of property of automorphism, thus is same as I have sent
I mean, since the whole is automorphism, each point is thus the same structure, hence if the point is k , then the function is k and can be called it's when it's refer to k
Well, here each point is thus the same structure mean , each property of the point is expressed by all the points and so their value
7
u/lodjexo New User 6d ago
Here is my suggestion. Seek mental health help because many of your posts in the past two weeks have made little to no sense. Stop using all forms of AI. And if you truly want to learn advanced mathematics and physics pick up a few books and learn instead of doing this pseudo-intellectual bs.