The Shintani Cocycle
نویسندگان
چکیده
منابع مشابه
Shintani Cocycles on GLn
The aim of this paper is to define an n− 1-cocycle σ on GLn(Q) with values in a certain space D of distributions on Af \ {0}. Here Af denotes the ring of finite adèles of Q, and the distributions take values in the Laurent series C((z1, . . . , zn)). This cocycle can be used to evaluate special values of Artin L-functions on number fields at negative integers. The construction generalizes that ...
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Suppose that G is a sheaf of groups on a space X and that Uα ⊂ X is an open covering. Then a cocycle for the covering is traditionally defined to be a family of elements gαβ ∈ G(Uα ∩ Uβ) such that gαα = e and gαβgβγ = gαγ when all elements are restricted to the group G(Uα ∩ Uβ ∩ Uγ). A more compact way of saying this is to assert that such a cocycle is a map of simplicial sheaves C(U)→ BG on th...
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The goal of this thesis is to generalize to elliptic curves a classical formula of Hecke. This is chiefly achieved through studying p-adic deformation of certain Shintani cycles attached to a real quadratic field K and an elliptic curve E/Q of conductor N . Assume that all the prime divisors of N are split in K. Also suppose that E has multiplicative reduction at a prime p, and denote by f E th...
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In this note, we describe various theoretical results, numerical computations, and speculations concerning the analytic properties of the Shintani zeta functions associated to the space of binary cubic forms. We describe how these zeta functions almost fit into the general analytic theory of zeta and L-functions, and we discuss the relationship between this analytic theory and counting problems...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1999
ISSN: 0022-314X
DOI: 10.1006/jnth.1998.2332