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1.
If , then let M k 0(4)) be the usual space of half integral weight modular forms. Ono constructed differential endomorphisms of M k 0(4)) by using the usual differential operator. Here we construct a similar set of differential endomorphisms using a linear combination of the differential operator and the quasi-modular forms E 2, E 2|V 2, and E 2|V 4. We compute a full set of eigenforms with eigenvalues, and we prove that these endomorphisms are in fact automorphisms. The author would like to thank the NSF for its support through the REGS program.  相似文献   

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Two classes of entire modular forms of weight 5 and two of weight 6 are constructed for the congruence subgroup 0(4N). The constructed modular forms as well as the modular forms from [1] will be helpful in the theory of representation of numbers by the quadratic forms in 10 and 12 variables.  相似文献   

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Entire modular forms of weights $\tfrac{7}{2}$ and $\tfrac{9}{2}$ for the congruence group Γ0(4N) are constructed, which will be useful for revealing the arithmetical sense of additional terms in formulas for the number of representations of positive integers by quadratic forms in 7 and 9 variables.  相似文献   

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We investigate degree two Siegel cusp forms of small weight for Γ0(p). Using the Restriction Technique we compute some dimensions and verify the conjectures ofHashimoto in some examples of weights three and four. For weight two we determine the dimension for primesp ≤ 41 and find only lifts. We explain in general how to compute spaces of Siegel cusp forms for subgroups of finite index in Γ n .  相似文献   

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The Ramanujan Journal - Let $$k ge 2$$ and N be positive integers and let $$chi $$ be a Dirichlet character modulo N. Let f(z) be a modular form in $$M_k(Gamma _0(N),chi )$$ . Then we have a...  相似文献   

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In (Katsurada in Math. Z. 259:97–111, 2008), we gave a certain type of normalization of the standard zeta values for Siegel modular forms, and considered the relationship between such values and congruence of cuspidal Hecke eigenforms. In this paper we give more reasonable normalization for such values and improve our previous result.  相似文献   

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Monatshefte für Mathematik - In this paper we prove a formula which relates the degree of a curve which is the image of a mapping $$zlongmapsto (f(z): g(z): h(z))$$ constructed out of three...  相似文献   

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We use the hyperbolic cotangent function to deduce another proof of Euler's formula for ζ(2n).  相似文献   

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Automorphic forms of arbitrary real weight can be considered as functions on the universal covering group of SL(2, ). In this situation, we prove an invariant form of the Selberg trace formula for Hecke operators. For this purpose, the Fourier transforms of weightet orbital integrals, obtained by J. Arthur, R. Herb and P. Sally, jr., are explicitly calculated. Our formula does not follow from Arthur's invariant trace formula, since the group has infinite centre, and vector-valued automorphic forms with respect to non-congruence lattices are considered.  相似文献   

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In a previous article, we proved that for a quadratic field, there are at most elliptic points on a Shimura curve of Γ0(p)-type for every sufficiently large prime number p. This is an analogue of the study of rational points on the modular curve X 0(p) by Mazur and Momose. In this article, we expand the previous result for Shimura curves to the case of number fields of higher degree, which seems unknown for X 0(p).  相似文献   

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LetB n be the unit ball inC n ,S is the boundary ofB n . We letL p (S) denote the usual Lebesgue spaces overS with respect to the normalized surface measure,H p (B n ) is its usua holomorphic subspace.H p (S) denotes the atomic Hardy spaces defined in [GL]. LetPL 2 (S)H 2(B n ) denote the orthogonal projection. For eachfL (S), we useM f L p (S)L p (S) to denote the multiplication operator, and we define the Toeplitz operatorT f =PM f . The paper gives a characterization theorem onf such that the Toeplitz operatorsT f and are bounded fromH p (S)H p (B n ) with 0<p1. Also several equivalent conditions are given.  相似文献   

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In this paper, we give the following dominated theorem: Let φ(g) ∈ L1(G//K),φε(t)=ε> 0, and the least radical decreasing dominatedfunction φ(t) = sup |φ(y)| ∈L1(G//K). If shtφ(t) is monotonically decreasingon (0, ∞), then for any f∈L1loc(G//K) , the following inequality holds:sup |φε * f(x)| ≤ Cmf(x),where mf(x) is the Hardy-Littlewood maximal function of f, and C = ||φ||1.An application of this dominated theorem is also given.  相似文献   

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In this paper, we find a basis for the space S k (?? 0(4)) of cusp forms of even weight k for the congruence subgroup ?? 0(4) in terms of Eisenstein series. As an application, we obtain formulas for r 4s (n), the number of ways to represent a nonnegative integer n as a sum of 4s integral squares.  相似文献   

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