共查询到20条相似文献,搜索用时 46 毫秒
1.
Min Ho Lee 《manuscripta mathematica》1991,73(1):163-177
We define the periods of mixed cusp forms and establish generalized Eichler-Shimura relations for the periods of mixed cusp
forms. We also construct modular symbols for mixed cusp forms and express the periods of mixed cusp forms in terms of these
modular symbols. 相似文献
2.
In this paper, we consider the space of second order cusp forms. We determine that this space is precisely the same as a certain subspace of mixed mock modular forms. Based upon Poincaré series of Diamantis and O’Sullivan (Trans. Am. Math. Soc. 360:5629–5666, 2008) which span the space of second order cusp forms, we construct Poincaré series which span a natural (more general) subspace of mixed mock modular forms. 相似文献
3.
Soumya Das 《Archiv der Mathematik》2010,95(5):423-437
We introduce a certain differential (heat) operator on the space of Hermitian Jacobi forms of degree 1, show its commutation
with certain Hecke operators and use it to construct a map from elliptic cusp forms to Hermitian Jacobi cusp forms. We construct
Hermitian Jacobi forms as the image of the tensor product of two copies of Jacobi forms and also from the differentiation
of the variables. We determine the number of Fourier coefficients that determine a Hermitian Jacobi form and use the differential
operator to embed a certain subspace of Hermitian Jacobi forms into a direct sum of modular forms for the full modular group. 相似文献
4.
WenZhi Luo 《中国科学 数学(英文版)》2010,53(9):2411-2416
In this note, we present a simple approach for bounding the shifted convolution sum involving the Fourier coefficients of half-integral weight holomorphic cusp forms and Maass cusp forms. 相似文献
5.
Alexandru A. Popa 《The Ramanujan Journal》2011,26(3):419-435
We prove explicit formulas decomposing cusp forms of even weight for the modular group, in terms of generators having rational
periods, and in terms of generators having rational Fourier coefficients. Using the Shimura correspondence, we also give a
decomposition of Hecke cusp forms of half integral weight k+1/2 with k even in terms of forms with rational Fourier coefficients, given by Rankin–Cohen brackets of theta series with Eisenstein
series. 相似文献
6.
O. M. Fomenko 《Journal of Mathematical Sciences》1991,53(3):323-338
Uniform estimates are given for Petersson's inner squares of cusp forms in the case of increasing levels and weights. The considered cusp forms are newforms or cusp forms occurring in the theta series associated with positive definite quadratic forms. Arithmetic applications of the obtained estimates are given.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 168, pp. 158–179, 1988. 相似文献
7.
In this paper we obtain some results on the gap function which measures the size of gaps in the Fourier expansion of cusp
forms that are not linear combinations of forms with complex multiplication. We also investigate the nonvanishing of Fourier
coefficients of such cusp forms along rational multiples of linear forms in two variables.
相似文献
8.
We give congruences between the Eisenstein series and a cusp form in the cases of Siegel modular forms and Hermitian modular forms. We should emphasize that there is a relation between the existence of a prime dividing the (k?1)th generalized Bernoulli number and the existence of non-trivial Hermitian cusp forms of weight k. We will conclude by giving numerical examples for each case. 相似文献
9.
Riccardo Salvati Manni 《manuscripta mathematica》2000,101(2):267-269
In this paper we prove the existence of cusp forms relative to the full modular group whose genus is equal to the weight.
These cusp forms are linear combination of theta series.
Received: 26 July 1999 / Revised version: 16 September 1999 相似文献
10.
In this article we study a Rankin‐Selberg convolution of n complex variables for pairs of degree n Siegel cusp forms. We establish its analytic continuation to ?n, determine its functional equations and find its singular curves. Also, we introduce and get similar results for a convolution of degree n Jacobi cusp forms. Furthermore, we show how the relation of a Siegel cusp form and its Fourier‐Jacobi coefficients is reflected in a particular relation connecting the two convolutions studied in this paper. As a consequence, the Dirichlet series introduced by Kalinin [7] and Yamazaki [19] are obtained as particular cases. As another application we generalize to any degree the estimate on the size of Fourier coefficients given in [14]. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
Goran Muić 《Mathematische Annalen》2009,343(1):207-227
In this paper we give a construction and study non-vanishing of a class of cusp forms using Poincaré series for a semisimple
algebraic group over a number field. 相似文献
12.
C. S. Yogananda 《Proceedings Mathematical Sciences》1993,103(1):1-25
In 1984 Jutila [5] obtained a transformation formula for certain exponential sums involving the Fourier coefficients of a holomorphic cusp form for the full modular groupSL(2, ?). With the help of the transformation formula he obtained good estimates for the distance between consecutive zeros on the critical line of the Dirichlet series associated with the cusp form and for the order of the Dirichlet series on the critical line, [7]. In this paper we follow Jutila to obtain a transformation formula for exponential sums involving the Fourier coefficients of either holomorphic cusp forms or certain Maass forms for congruence subgroups ofSL(2, ?) and prove similar estimates for the corresponding Dirichlet series. 相似文献
13.
Koichi Takase 《Transactions of the American Mathematical Society》1999,351(2):735-780
We will establish a bijective correspondence between the space of the cuspidal Jacobi forms and the space of the half-integral weight Siegel cusp forms which is compatible with the action of the Hecke operators. This correspondence is based on a bijective correspondence between the irreducible unitary representations of a two-fold covering group of a symplectic group and a Jacobi group (that is, a semidirect product of a symplectic group and a Heisenberg group). The classical results due to Eichler-Zagier and Ibukiyama will be reconsidered from our representation theoretic point of view.
14.
V. A. Gritsenko 《Journal of Mathematical Sciences》1987,38(4):2065-2078
One constructs an integral operator, mapping the cusp modular forms of one variable into modular forms relative to Hermitian groups of genus 2 over an imaginary quadratic field. One computes explicitly the Fourier coefficients of the obtained forms.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 144, pp. 51–67, 1985. 相似文献
15.
16.
令λ(n)为SL_2(Z)上全纯尖形式所对应的傅里叶系数.本文研究了全纯尖形式傅里叶系数与素变量多项式的混合问题,并给出和式∑n=p_1~k+p_2~2+p_3~2≤xλ(n) and ∑ n=p_1~k+p_2~2+p_3~2≤xλ(n)Λ(n)的上界估计. 相似文献
17.
In this paper, we discuss the dimension formula for Jacobi forms via the Selberg trace formula, an explicit dimension formula
for the space of Jacobi cusp forms of degree 2 is given as an application. 相似文献
18.
In this paper, we construct Shintani lifts from integral weight weakly holomorphic modular forms to half-integral weight weakly holomorphic modular forms. Although defined by different methods, these coincide with the classical Shintani lifts when restricted to the space of cusp forms. As a side effect, this gives the coefficients of the classical Shintani lifts as new cycle integrals. This yields new formulas for the L-values of Hecke eigenforms. When restricted to the space of weakly holomorphic modular forms orthogonal to cusp forms, the Shintani lifts introduce a definition of weakly holomorphic Hecke eigenforms. Along the way, auxiliary lifts are constructed from the space of harmonic weak Maass forms which yield a “fractional derivative” from the space of half-integral weight harmonic weak Maass forms to half-integral weight weakly holomorphic modular forms. This fractional derivative complements the usual ξ-operator introduced by Bruinier and Funke. 相似文献
19.
王巨平 《中国科学A辑(英文版)》2002,45(7):827-835
This paper verifies the singularity conjecture for Jacobi forms with higher degree in some typical cases, and gives constructions
for the Jacobi cusp forms whose Fourier coefficients can be expressed by some kind of Rankin-typeL-series. 相似文献
20.
Wen-Ching Winnie Li 《Journal of Number Theory》2008,128(7):1941-1965
In this paper, we study the Drinfeld cusp forms for Γ1(T) and Γ(T) using Teitelbaum's interpretation as harmonic cocycles. We obtain explicit eigenvalues of Hecke operators associated to degree one prime ideals acting on the cusp forms for Γ1(T) of small weights and conclude that these Hecke operators are simultaneously diagonalizable. We also show that the Hecke operators are not diagonalizable in general for Γ1(T) of large weights, and not for Γ(T) even of small weights. The Hecke eigenvalues on cusp forms for Γ(T) with small weights are determined and the eigenspaces characterized. 相似文献