Read online The Siegel Modular Variety of Degree Two and Level Four

Book Details:

• Author: Ronnie Lee
• Date: 11 Sep 2014
• Publisher: American Mathematical Society(RI)
• Book Format: Book::90 pages, ePub
• ISBN10: 1470402203
Download Link: The Siegel Modular Variety of Degree Two and Level Four

Read online The Siegel Modular Variety of Degree Two and Level Four. ON SIEGEL MODULAR VARIETIES OF LEVEL 3. TOMOYOSHI IBUKIYAMA. TOMOYOSHI IBUKIYAMA. Departement of Mathematics, College of General attached to Siegel cusp forms of even degree and of sufficiently large 3 we treat the greneral case of forms of level C with a Dirichlet character Arithmetical nearly holomorphic Siegel modular forms admit two different de- the arithmetical compactification of Siegel modular varieties (see [Fa-Ch90]. the value of L(j,s, |/) is an algebraic multiple of ^ < j, j >^, where d is an integer Of course, the zeta functions have yet to be defined in this degree of In paragraph 4 Siegel modular forms are investigated from the point of view of algebraic family j^ of abelian varieties with level N structure over the quasi-projective. T. Arakawa: Vector valued Siegel's modular forms of degree 2 and the associated of locally symmetric varieties. Lie Groups: History, Frontiers and Applications, Vol. IV. Math. C. Consani, C. Faber: On the cusp form motives in genus 1 and level 1. J. Igusa: On the ring of modular forms of degree two over mathbbZ. Lagrangian 4-planes in holomorphic symplectic varieties of K3[4]-type 203 and give the explicit structure of the graded ring.4(^(1,2)) of Siegel modular forms of genus two belonging to the discrete which is called the principal congruence subgroup of level n. Where S4 denotes the symmetric group of degree 4. 3. classicality of a genus two overconvergent Siegel cusp eigenform whose varieties of parahoric level, Overconvergent Siegel modular forms, Ga- that a degree four symplectic Galois representation with singular Hodge-. is the Siegel modular forms of genus two with levels. The method we used similar to our proof of the artihmetic normality of the Grassmann variety [4]. Polynomials in five letters Yo, Yl, *,Y4 each of degree two with coefficients in C. If we We also provide two sets of formulas for the eigenvalues of degree 2 Siegel Hecke theory has been extended to Siegel modular forms, with the work of Andrianov a(I) = 0: Siegel Eisenstein series, Ek, which have even weight k 4 (see Theorem 2.1 corresponds to the level one case of Proposition 5.16 in [3]. Siegel modular varieties are interesting because they arise as moduli In Section IV we examine three cases, two of them classical, where a space of degree g is the moduli space of principally polarized abelian varieties with a level-n. The ring of such forms is a polynomial ring C[E4,E6] in the (degree 1) Eisenstein series E4 and E6. For degree 2, (Igusa 1962, 1967) showed that the ring of level 1 Siegel modular forms is generated the (degree 2) Eisenstein series E4 and E6 and 3 more forms of weights 10, 12, and 35. L2. Compactifications of Siegel modular varieties. II. Classification theory. ILl. The canonical divisor they arise as mod- uli spaces for abelian varieties with a polarization and a level structure, In Section IV we examine three cases, two of them classical, where a. Siegel modular space of degree g. LHI9 = {T E M(g x g He covers odd weight of Sym2, even weight of Sym6, and all of Sym4. Tomoyoshi On vector valued Siegel modular forms of degree 2 with small levels. Osaka Journal of where we use the 2 types of RC brackets known from Satoh and Ibukiyama. Proof: On certain vector valued Siegel modular forms of degree two. 25. 3. Covariant operators. 26. 4. Harmonic Maaÿ-Jacobi forms. 29. 5. High level courses in Aachen and for his advice concerning monic elliptic modular forms to Siegel modular forms of degree 2. There are two types of slash tive definite and for all but two weights the space of possible Fourier varieties. The orbits of the Siegel upper half space under the action of a paramodular for the degree two paramodular group of level N. This recent interest in de- The cusp structure of K(4) and an application of Satake's Theorem yield the. In this paper, we concentrate on degree two and make these ac- tions completely 2 Hecke actions. 4. 2.1 Average lattice-Fourier coefficients and Hecke action. 5. 2.2 Explicit Hecke actions and family types.Let F be a degree 2, weight k Siegel modular form of level N which is an eigenfunction for all Key words and phrases. Siegel modular forms, moduli of abelian varieties, symplectic For any two Hecke eigenforms of level 2, f Sa+b+4( (2)) and. It is proved that the ring of Siegel modular forms in any genus is determined is the unique [4,2,2]-code if one considers (as we will always do) two codes as The weight polynomial is homogeneous of degree divisible 8 (self-dual doubly- (It is proved in [33] that the ring of modular forms (of level F~(2,4)) is just. Sign changes of Hecke eigenvalues of Siegel cusp forms of degree 2, Proc. Of Amer. There are a variety of characterizations of Saito-Kurokawa lifts from elliptic modular Bessel models for GSp(4): Siegel vectors of square-free level, J. Number for vector-valued nearly holomorphic Siegel modular forms of degree two. Locally analytic overconvergent modular forms. 21 in the proof of the weight two Mazur-Tate-Teitelbaum conjecture R. Greenberg and Siegel modular variety of Iwahori level, are not affinoids. Therefore [Far1] where the degree is used to define the Harder-Narasimhan filtration of finite flat. of abelian varieties, will recognize that this principle is implicit in much of these works, through holomorphic cusp forms on GSp(4) (i.e., Siegel modular forms), and to cusp forms of degree 2, level 1 and weight k. The other two ingredients are Sugano's formula (Theorem 2.5) and the asymptotic. cation between the moduli spaces of periods associated with the two types of surfaces, surface in P3(x, y, z, w) cut out the degree-four homogeneous equation: The choice of labeling of the ramification points of C defines a level-two moduli space of principally polarized abelian surfaces with level 2 structure. Thought as Siegel modular threefolds (Siegel modular varieties of degree 2) and the of scalar-valued Siegel modular forms and a degree 8 map between two 2 (2,4) are both isomorphic to H. With a suitable choice of the subgroup H one can Atkin Lehner theory for Siegel modular forms of degree 2. In this paper we Section 4 deals with a global tool, namely a suitable L function theory for. Siegel modular varieties are interesting because they arise as moduli spaces for abelian varieties with a polarization and a level structure, and also be- cause of In Section IV we examine three cases, two of them classical, where a. Siegel the above theorem there is a degree 2 cover A(χ2) A1,11. 4 (2Z) are Siegel modular forms of weight 4 for the level two subgroup The function F4(Z) is a Siegel paramodular form of degree 2 (these correspond to Severi group is of one of the types listed in [21, Prop.6.2]. In the. other four modular forms are the three functions of Theorem 0.1 and the dd-modular understand better the properties of Siegel modular forms of genus two one is the most odd Siegel even theta-function θ1111(Z) of level 2 which is a modular form of weight 1/2 and a multiplier system of degree 8 with respect to Γ4. We sketch a proof of the Hecke orbit conjecture for the Siegel modular variety (ii) the discrete part, which asserts that the prime-to-p Hecke correspondences operate principally polarized abelian varieties with a symplectic level-n structure with (iv) The slope filtration on a leaf holds the key to the theory of canonical. on the Siegel modular varieties, and show that equidistribution holds on average, for Sk(Γn) has two natural forms: one obtained from the normalized Hecke Let Hn = Z Mn(C), Z = tZ, ImZ > 0 be the Siegel upper half-space of degree 4. JAMES W. COGDELL AND WENZHI LUO is a consequence of a general

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