A Stickelberger theorem for p-adic Gauss sums
نویسندگان
چکیده
منابع مشابه
A STICKLEBERGER THEOREM FOR p-ADIC GAUSS SUMS
Character sums over finite fields have been widely studied since Gauss. During the last decade, coding theorists initiated the study of a new type of sums, over points with coordinates in a p-adic field. Let O (u) m be the ring of integers of Q p(ζpm−1), the unramified extension of degree m of the field of p-adic numbers Q p obtained by adjoining the (p−1)-th roots of unity, Tm = T ∗ m∪{0}, whe...
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Let F be a non-Archimedean local field. LetG stand for the F -points of a connected reductive algebraic group defined over F . We will refer to G as a p-adic group, with the understanding that the base field F is fixed once and for all. We let R(G) denote the category of smooth complex representations of G. It is well known [1] that this is an abelian category and has enough projectives and hen...
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The T -adic deformation of p-adic exponential sums is defined. It interpolates all classical p-power order exponential sums over a finite field. Its generating L-function is a T -adic entire function. We give a lower bound for its T -adic Newton polygon and show that the lower bound is often sharp. We also study the variation of this L-function in an algebraic family, in particular, the T -adic...
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The notion of relative cuspidality for distinguished representations attached to p-adic symmetric spaces is introduced. A characterization of relative cuspidality in terms of Jacquet modules is given and a generalization of Jacquet’s subrepresentation theorem to the relative case (symmetric space case) is established.
متن کامل2 A CERTAIN p - ADIC SPECTRAL THEOREM
3 ABSTRACT. We extend a p-adic spectral theorem of M. M. Vishik to a certain class of p-adic Banach algebras. This class includes inductive limits of finite-dimensional p-Banach algebras of the form B(X), where X is a p-adic Banach space of the form X ≃ Ω p (J), J being a finite nonempty set. In particular, we present a p-adic spectral theorem for p-adic UHF algebras and p-adic TUHF algebras (T...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2005
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa118-1-2