On Eisenstein ideals and the cuspidal group of J0(N)

Let C_N be the cuspidal subgroup of the Jacobian J₀(N) for a square-free integer N > 6. For any Eisenstein maximal ideal m of the Hecke ring of level N, we show that C_N[m] ≠ 0. To prove this, we calculate the index of an Eisenstein ideal I contained in m by computing the order of the cuspidal divisor annihilated by I.     

The old subvariety ofJ 0(pq) and the Eisenstein kernel in Jacobians

Whenp, q are distinct odd primes, and γ:J ₀(p)²×J ₀(q)²→J ₀(pq) is the natural map defined by the degeneracy maps, Ribet [10] determined the odd part of the kernel of γ. We study the 2-primary part of this kernel through its intersection with the Eisenstein kernelJ ₀(p)[I _p )²×J ₀(q)[I _q ]². We determine this intersection forp≢1 mod 16,q≢1 mod 16, and also produce new elements of ker γ wheneverp≡9 mod 16 orq≡9 mod 16. These sharpen Ribet's results in [10].     

Eisenstein series for SL(2)

This paper gives explicit formulas for the Fourier expansion of general Eisenstein series and local Whittaker functions over SL₂. They are used to compute both the value and derivatives of these functions at critical points.     

Eisenstein series on quaternion half-space of degree N

In Kim [7], we studied an Eisenstein series on quaternion half-space of degree 2. By calculating the Siegel series using the method of Karel [5], we obtained the analytic continuation and functional equation of the Eisenstein series. In this note we study an Eisenstein series on quaternion half-space of degreen. By calculating the Siegel series in an analogous way as in Shimura [15] and Kitaoka [8], we obtain singular modular forms of weightk, k<2n and 4/k. Furthermore, we obtain the analytic continuation and functional equation of the Eisenstein series.     

On primitive elements of algebraic function fields and models of $$X_0(N)$$ X 0 ( N )

The Ramanujan Journal - This paper is a continuation of our previous works where we study maps from $$X_0(N)$$ , $$Nge 1$$ , into $${mathbb {P}}^2$$ constructed via modular forms of the same...     

2-dimensional simple factors ofJ 0(N)

In this paper we investigate abelian varietyA _f which is derived from a newformf ∈ S ₂(Г₀(N)) an is ℚ-simple factors ofJac(X ₀ (N)). We will develop algorithms for computing the period matrix ofA _f and for determing whenA _f is principally polarized. IfA _f is 2-dimensional principally polarized, we give an algorithm for computing the associated hyperelliptic curveC withJac(C)≊A _f.     

Über die Automorphismengruppe vonX 0(N)

Ohne Zusammenfassung     

Polar Decompositions of C 0(N) Contractions

Let A be a bounded linear operator on a complex separable Hilbert space H. We show that A is a C₀(N) contraction if and only if , where U is a singular unitary operator with multiplicity and x₁, . . . , x_d are orthonormal vectors satisfying . For a C₀(N) contraction, this gives a complete characterization of its polar decompositions with unitary factors.     

关于图B（m,n,p）的优美性

在［１］［２］中已证明“除去三种特殊情形，连结两个顶点的三条独立路所成简单图Ｂ（ｍ，ｎ，ｐ）是优美图”，并猜想：对除去的三种情形，Ｂ（ｍ，ｎ，ｐ）也是优美的。本文证实了上术猜想。这样一来，也就证明了［３］中的猜想：有－ｈ－链弦的圈是优美的（ｈ≥２）。     

Modulformen auf Γ0(N) mit rationalen Periodenmit rationalen Perioden

Ohne Zusammenfassung     

The Kernel of the Eisenstein Ideal

Let N be a prime number, and let J₀(N) be the Jacobian of the modular curve X₀(N). Let T denote the endomorphism ring of J₀(N). In a seminal 1977 article, B. Mazur introduced and studied an important ideal I⊆T, the Eisenstein ideal. In this paper we give an explicit construction of the kernel J₀(N)[I] of this ideal (the set of points in J₀(N) that are annihilated by all elements of I). We use this construction to determine the action of the group Gal(Q/Q) on J₀(N)[I]. Our results were previously known in the special case where N−1 is not divisible by 16.     

GM(1,N)与GM(0,N)模型在能源消费碳排放预测中的比较研究

近年来,减少碳排放已成为缔约国家社会经济发展和生产经营活动的重要目标之一,研究并使用科学的方法对我国未来碳排放进行分析与预测对我国应对气候变化政策的制定具有重要意义.拟将GM(1,N)和GM(0,N)模型用于能源消费碳排放量的预测,建立能源消费碳排放量的多因素灰色预测模型,并对GM(1,N)和GM(0,N)模型预测能源消费碳排放量的精度进行了检验和对比分析.结果表明:在对四川省能源消费碳排放预测中,GM(0,N)具有更高的预测精度和可靠性.     

B(0, N)-graded Lie superalgebras coordinatized by quantum tori

We use a fermionic extension of the bosonic module to obtain a class of B(0, N)graded Lie superalgebras with nontrivial central extensions.     

Points de petite hauteur sur les courbes modulaires X0(N)

Let N be a square free integer, prime to 6. Let φ the imbeding of X ₀(N) in its Jacobian relative to the point ∞. We show that the set is finite and that is infinite. This explicit form of the Bogomolov conjecture is obtained by an estimation of the self-intersection of the dualizing sheaf, in the sense of Arakelov theory, of modular curves. This result is obtained by estimating several quantities attached to the Arakelov metric on X ₀(N), starting with Petersson's trace formula Oblatum 1-I-1997 & 30-IV-1997     

Fourier coefficients of real analytic Eisenstein series at various cusps (II)

The Ramanujan Journal - The purpose of this paper is to consider the computation of the Fourier coefficients of real-analytic Eisenstein series associated to general cusps of Hecke congruence...     

关于艾森斯坦因判别法的间接应用

探讨了间接应用艾森斯坦因判别法判断整系数多项式在有理数域上不可约的两种途径.