共查询到20条相似文献,搜索用时 31 毫秒
1.
Hae-Sang Sun 《Journal of Number Theory》2010,130(1):10-26
We extend the result of Anglès (2007) [1], namely for the Iwasawa power series . For the derivative , a numerical polynomial Q on Zp, and a prime π in over p, we show that if and only if i.e. for all x∈Zp. This result comes from a similar assertion for the power series attached to the Γ-transform of a p-adic measure which is related to a certain rational function in . 相似文献
2.
Jayanta Manoharmayum 《Journal of Number Theory》2009,129(5):1178-1190
Let F be a number field. Given a continuous representation with insoluble image we show, under moderate assumptions at primes dividing ?∞, that for some continuous representation which is unramified outside finitely many primes. We also establish level lowering when F is totally real, is the reduction of a nearly ordinary Hilbert modular form and is distinguished at ?. 相似文献
3.
Kui Liu 《Journal of Number Theory》2011,131(12):2247-2261
Let be the error term of the Riesz mean of the symmetric square L-function. We give the higher power moments of and show that if there exists a real number A0:=A0(ρ)>3 such that , then we can derive asymptotic formulas for , 3?h<A0, h∈N. Particularly, we get asymptotic formulas for , h=3,4,5 unconditionally. 相似文献
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Najib Ouled Azaiez 《Journal of Number Theory》2008,128(7):1966-1988
We describe the additive structure of the graded ring of quasimodular forms over any discrete and cocompact group Γ⊂PSL(2,R). We show that this ring is never finitely generated. We calculate the exact number of new generators in each weight k. This number is constant for k sufficiently large and equals where I and are the ideals of modular forms and quasimodular forms, respectively, of positive weight. We show that is contained in some finitely generated ring of meromorphic quasimodular forms with i.e., the same order of growth as 相似文献
6.
Siham Bekkai 《Discrete Applied Mathematics》2010,158(17):1888-1893
We bound the mean distance in a connected graph which is not a tree in terms of its order n and its girth g. On one hand, we show that the mean distance is at most if g is even and at most if g is odd. On the other hand, we prove that the mean distance is at least unless G is an odd cycle. This resolves two conjectures of AutoGraphiX. 相似文献
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8.
Yingjue Fang 《Journal of Number Theory》2011,131(11):2078-2080
Let E be a finite dimensional symplectic space over a local field of characteristic zero. We show that for every element in the metaplectic double cover of the symplectic group Sp(E), and are conjugate by an element of GSp(E) with similitude −1. 相似文献
9.
We define and investigate extension groups in the context of Arakelov geometry. The “arithmetic extension groups” we introduce are extensions by groups of analytic types of the usual extension groups attached to OX-modules F and G over an arithmetic scheme X. In this paper, we focus on the first arithmetic extension group - the elements of which may be described in terms of admissible short exact sequences of hermitian vector bundles over X - and we especially consider the case when X is an “arithmetic curve”, namely the spectrum SpecOK of the ring of integers in some number field K. Then the study of arithmetic extensions over X is related to old and new problems concerning lattices and the geometry of numbers.Namely, for any two hermitian vector bundles and over X:=SpecOK, we attach a logarithmic size to any element α of , and we give an upper bound on in terms of slope invariants of and . We further illustrate this notion by relating the sizes of restrictions to points in P1(Z) of the universal extension over to the geometry of PSL2(Z) acting on Poincaré's upper half-plane, and by deducing some quantitative results in reduction theory from our previous upper bound on sizes. Finally, we investigate the behaviour of size by base change (i.e., under extension of the ground field K to a larger number field K′): when the base field K is Q, we establish that the size, which cannot increase under base change, is actually invariant when the field K′ is an abelian extension of K, or when is a direct sum of root lattices and of lattices of Voronoi's first kind.The appendices contain results concerning extensions in categories of sheaves on ringed spaces, and lattices of Voronoi's first kind which might also be of independent interest. 相似文献
10.
We exhibit a genus-2 curve defined over which admits two independent morphisms to a rank-1 elliptic curve defined over . We describe completely the set of -rational points of the curve and obtain a uniform bound on the number of -rational points of a rational specialization of the curve for a certain (possibly infinite) set of values . Furthermore, for this set of values we describe completely the set of -rational points of the curve . Finally, we show how these results can be strengthened assuming a height conjecture of Lang. 相似文献
11.
Zhi-Hong Sun 《Journal of Number Theory》2008,128(2):280-312
Let [x] be the integral part of x. Let p>5 be a prime. In the paper we mainly determine , , and in terms of Euler and Bernoulli numbers. For example, we have
12.
Guangshi Lü 《Journal of Number Theory》2010,130(10):2147-2156
Let a be an integral ideal in a quaternion algebra U over rational numbers Q which ramifies precisely at p and ∞, and d(a) be its divisor function. Recently, Kim and Zhang proved a quaternion analogue of the classical formula , and then established an asymptotic formula for the sum . In this note we improved the upper bound for the error term in the asymptotic formula, and then considered the quaternion analogue of another well-known formula . 相似文献
13.
Let be a finite field with q=pfelements, where p is a prime number and f is a positive integer. For a nonprincipal multiplicative character χ and a nontrivial additive character ψ on , it is well known that Gauss sum has absolute value . In this paper, we investigate when is a root of unity. 相似文献
14.
Jeffrey Lin Thunder 《Journal of Number Theory》2003,101(2):294-309
For homogeneous decomposable forms in n variables with real coefficients, we consider the associated volume of all real solutions to the inequality . We relate this to the number of integral solutions to the Diophantine inequality in the case where F has rational coefficients. We find quantities which bound the volume and which yield good upper bounds on the number of solutions to the Diophantine inequality in the rational case. 相似文献
15.
Norisato Kataoka 《Journal of Number Theory》2003,101(2):349-375
Let k be a real quadratic number field and the ring of integers and the group of units in k. Denote by the subgroup represented by elements of E of for a prime ideal in k. We show that for a given positive rational integer a, the set of prime numbers p for which the residual index of for lying above p is equal to a has a natural density c under the Generalized Riemann Hypothesis. Moreover, we give the explicit formula of c and conditions to c=0. 相似文献
16.
Alex V. Kontorovich 《Journal of Number Theory》2006,117(1):1-13
For every positive integer n, the quantum integer [n]q is the polynomial [n]q=1+q+q2+?+qn-1. A quadratic addition rule for quantum integers consists of sequences of polynomials , , and such that for all m and n. This paper gives a complete classification of quadratic addition rules, and also considers sequences of polynomials that satisfy the associated functional equation . 相似文献
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For a given finite monoid , let be the number of graphs on n vertices with endomorphism monoid isomorphic to . For any nontrivial monoid we prove that where and are constants depending only on with .For every k there exists a monoid of size k with , on the other hand if a group of unity of has a size k>2 then . 相似文献
19.
Zhi-Hong Sun 《Journal of Number Theory》2009,129(3):499-550
Let be a prime and a,b∈Z with a2+b2≠p. Suppose p=x2+(a2+b2)y2 for some integers x and y. In the paper we develop the calculation technique of quartic Jacobi symbols and use it to determine . As applications we obtain the congruences for modulo p and the criteria for (if ), where {Un} is the Lucas sequence given by U0=0, U1=1 and Un+1=bUn+k2Un−1(n?1). We also pose many conjectures concerning , or . 相似文献
20.
H. Kisilevsky 《Journal of Number Theory》2004,104(2):279-286
Suppose that E1 and E2 are elliptic curves over the rational field, , such that for all quadratic fields . We prove that their conductors N(E1), and N(E2) are equal up to squares. If for all quadratic fields , then the same conclusion holds, provided the 2-parts of their Tate-Shafarevich groups are finite. 相似文献