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1.
Let χ be an order c multiplicative character of a finite field and f(x)=xd+λxe a binomial with (d,e)=1. We study the twisted classical and T-adic Newton polygons of f. When p>(de)(2d1), we give a lower bound of Newton polygons and show that they coincide if p does not divide a certain integral constant depending on pmodcd.We conjecture that this condition holds if p is large enough with respect to c,d by combining all known results and the conjecture given by Zhang-Niu. As an example, we show that it holds for e=d1.  相似文献   
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3.
Let λ(n) be the n-th normalized Fourier coeficient of a holomorphic Hecke eigenform f(z) ∈ Sk(Γ) for the full modular group.In one of his papers,Sankaranarayanan mentioned that it is an open problem to give a non-trivial estimate for the sum of λ(n) over cubes,i.e.n x λ(n3).In this paper,we are able to use the analytic properties of symmetric power L-functions to solve his problem.More precisely,we prove that Σn≤zλ(n3) x(3/4 +ε),Σn≤zλ(n4) x(97+ε).  相似文献   
4.
51. Notations and IntroductionListed below are some general notations which wi1l be used thIoughout this note:pea prime number greater than 3,cl l, mt r, s E N,(:) = n!/(kl(n -- k)!)--the binomial coefficient,Bk--the kth Bernoulli number in the "even suthe" notation, e.g., Bo = 1, B1 =--1/2, B2 = 1/6, B3 = 0,',B.(x) = Z (:)Bkx"--*--the Bernoulli polynomial.k=0As is known, the Bernoulli numbers are defined by the symbolic recurrence relationB.+l = (B + 1)"+', n = 1, 2,', Bo = l, whic…  相似文献   
5.
We give a decomposition formula for the determinant det(I ? U(λ)) of the weighted bond scattering matrix U(λ) of a regular covering of G. Furthermore, we define an L-function of G, and give a determinant expression of it. As a corollary, we express some determinant of the weighted bond scattering matrix of a regular covering of G by means of its L-functions.  相似文献   
6.
The authors establish an explicit formula for the generalized Euler NumbersE2n^(x), and obtain some identities and congruences involving the higher'order Euler numbers, Stirling numbers, the central factorial numbers and the values of the Riemann zeta-function.  相似文献   
7.
He  Yuan 《数学学报(英文版)》2019,35(9):1549-1562
In this paper, by making use of Abel's theorem on power series, the reflection formula and the function equation for Hurwitz zeta function, we establish several expressions of Dirichlet L-function at positive integers by means of some finite sums of different types. Some special cases as well as immediate consequences of the results presented here are also considered.  相似文献   
8.
华国栋 《数学进展》2021,(1):117-124
取f为权为偶数k的全模群Γ=SL(2,Z)的Hecke特征型.定义λsymmf(n)为与f关联的m阶对称幂次L-函数的Dirichlet展开式的第n个正规化系数.本文中,我们给出了∑n≤x max{|λsymmf(n)|,|λsymmf(n+h)|}的上下界,其中h为一个固定的正整数,β> 0为一个正数.  相似文献   
9.
A Voronin-type discrete universality theorem for the L-functions of new forms is proved.  相似文献   
10.
设0<ε<1/(6log10),x为模k的实原特征且k大于e1/ε.则除去至多一个可能的例外特征外,均有这改进了Hoffstein等人的结果.  相似文献   
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