منابع مشابه
Background on Weil Descent
CRC Press has granted the following specific permissions for the electronic version of this book: Permission is granted to retrieve a copy of this chapter for personal use. This permission does not extend to binding multiple chapters of the book, photocopying or producing copies for other than personal use of the person creating the copy, or making electronic copies available for retrieval by o...
متن کاملWeil Conjecture I
Solving Diophantine equation is one of the main problem in number theory for a long time. It is very difficult but wonderful. For example, it took over 300 years to see that Xn + Y n = Zn has no nontrivial integers solution when n ≥ 3. We would like to consider an easier problem: solving the Diophantine equation modulo p, where p is a prime number. We expect that this problem is easy enough to ...
متن کاملWeil Converse Theorem
Hecke generalized this equivalence, showing that an integral form has an associated Dirichlet series which can be analytically continued to C and satisfies a functional equation. Conversely, Weil showed that, if a Dirichlet series satisfies certain functional equations, then it must be associated to some integral form. Our goal in this paper is to describe this work. In the first three sections...
متن کاملQuadratic Reciprocity , after Weil
The character associated to a quadratic extension field K of Q, χ : Z −→ C, χ(n) = (disc(K)/n) (Jacobi symbol), is in fact a Dirichlet character; specifically its conductor is |disc(K)|. This fact encodes basic quadratic reciprocity from elementary number theory, phrasing it in terms that presage class field theory. This writeup discusses Hilbert quadratic reciprocity in the same spirit. Let k ...
متن کاملThe Weil bounds
• Y 2 −X is reducible, • Y 2 − αX is irreducible, but not absolutely irreducible, • Y 2 −X + 1 is absolutely irreducible. To see the last item, note that any factorization of H(X,Y ) = Y −X+1 in F[X,Y ] is also a factorization of H(X,Y ) in K[Y ], where K is the field F(X), and thus the factorization must be of the form (Y −a(X))(Y + a(X)), where a(X) ∈ K satisfies a(X) = X − 1. But this cannot...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Religija ir kultūra
سال: 2017
ISSN: 1822-4539,1822-4539
DOI: 10.15388/relig.2014.14-15.10830