L-FUNCTIONS OF p-ADIC CHARACTERS
نویسندگان
چکیده
We define a p-adic character to be a continuous homomorphism from 1 + tFq [[t]] to Zp. For p > 2, we use the ring of big Witt vectors over Fq to exhibit a bijection between p-adic characters and sequences (ci)(i,p)=1 of elements in Zq , indexed by natural numbers relatively prime to p, and for which limi→∞ ci = 0. To such a p-adic character we associate an L-function, and we prove that this L-function is p-adic meromorphic if the corresponding sequence (ci) is overconvergent. If more generally the sequence is C log-convergent, we show that the associated L-function is meromorphic in the open disk of radius qC . Finally, we exhibit examples of C log-convergent sequences with associated L-functions which are not meromorphic in the disk of radius qC+ for any > 0.
منابع مشابه
p-ADIC L-FUNCTIONS: THE KNOWN AND UNKNOWN
1. Iwasawa functions, p-adic measures, and distributions 1 1.1. Some preliminaries 1 1.2. Iwasawa functions and the Iwasawa algebra 3 1.3. Iwasawa functions and interpolation 4 1.4. p-adic distributions and p-adic measures 8 2. The p-adic L-functions of Dirichlet characters 10 2.1. Preliminaries 10 2.2. Iwasawa’s construction 12 3. The p-adic L-functions of modular forms 15 3.1. Preliminaries 1...
متن کامل$p$-adic Dual Shearlet Frames
We introduced the continuous and discrete $p$-adic shearlet systems. We restrict ourselves to a brief description of the $p$-adic theory and shearlets in real case. Using the group $G_p$ consist of all $p$-adic numbers that all of its elements have a square root, we defined the continuous $p$-adic shearlet system associated with $L^2left(Q_p^{2}right)$. The discrete $p$-adic shearlet frames for...
متن کاملp-adic Shearlets
The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.
متن کاملThe rationality of Stark-Heegner points over genus fields of real quadratic fields
We study the algebraicity of Stark-Heegner points on a modular elliptic curve E. These objects are p-adic points on E given by the values of certain p-adic integrals, but they are conjecturally defined over ring class fields of a real quadratic field K. The present article gives some evidence for this algebraicity conjecture by showing that linear combinations of Stark-Heegner points weighted b...
متن کاملNumerical Evidence Toward a 2-adic Equivariant "Main Conjecture"
1. The conjecture Let K be a totally real finite Galois extension of Q with Galois group G dihedral of order 8, and suppose that √ 2 is not in K. Fix a finite set S of primes of Q including 2, ∞ and all primes that ramify in K. Let C be the cyclic subgroup of G of order 4 and F the fixed field of C acting on K. Fix a 2-adic unit u ≡ 5 mod 8Z 2. Write L F (s, χ) for the 2-adic L-functions, norma...
متن کامل