On the Symmetric Powers of the p-adic Airy family
نویسنده
چکیده
For each positive integer k, using techniques of Dwork’s, we investigate the L-function defined by the k-th symmetric power of the F -crystal associated to the family of exponential sums of x + λx where λ runs over F ∗ p. In particular, we will explore its rationality, coefficients, degree, trivial factors, functional equation, and Newton polygon.
منابع مشابه
L-functions of symmetric powers of the generalized Airy family of exponential sums: l-adic and p-adic methods
For ψ a nontrivial additive character on the finite field Fq, observe that the map t 7→ P x∈Fq ψ(f(x) + tx) is the Fourier transform of the map t 7→ ψ(f(t)). As is well-known, this has a cohomological interpretation, producing a continuous l-adic Galois representation. This paper studies the L-function attached to the k-th symmetric power of this representation using both l-adic and p-adic meth...
متن کاملOn Symmetric Power L-invariants of Iwahori Level Hilbert Modular Forms
We compute the arithmetic L-invariants (of Greenberg–Benois) of twists of symmetric powers of p-adic Galois representations attached to Iwahori level Hilbert modular forms (under some technical conditions). Our method uses the automorphy of symmetric powers and the study of analytic Galois representations on p-adic families of automorphic forms over symplectic and unitary groups. Combining thes...
متن کاملL-functions of symmetric powers of cubic exponential sums
For each positive integer k, we investigate the L-function attached to the k-th symmetric power of the F -crystal associated to the family of cubic exponential sums of x + λx where λ runs over Fp. We explore its rationality, field of definition, degree, trivial factors, functional equation, and Newton polygon. The paper is essentially self-contained, due to the remarkable and attractive nature ...
متن کاملSUPER-APPROXIMATION, II: THE p-ADIC AND BOUNDED POWER OF SQUARE-FREE INTEGERS CASES
Let Ω be a finite symmetric subset of GLn(Z[1/q0]), Γ := 〈Ω〉, and let πm be the group homomorphism induced by the quotient map Z[1/q0] → Z[1/q0]/mZ[1/q0]. Then the family of Cayley graphs {Cay(πm(Γ), πm(Ω))}m is a family of expanders as m ranges over fixed powers of square-free integers and powers of primes that are coprime to q0 if and only if the connected component of the Zariski-closure of ...
متن کاملSymmetric powers and the Satake transform
This paper gives several examples of the basic functions introduced in recent years by Ng^o. These are mainly conjectures based on computer experiment.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008