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Siegfried Böcherer Shoyu Nagaoka 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2010,80(2):227-231
J.-P. Serre proved that the congruences for elliptic modular forms mod p
m
descend to those of weights mod p
m−1(p−1). Later, this result was generalized by T. Ichikawa to the case of Siegel modular forms. In this note we use elementary
methods to reduce Ichikawa’s result to a similar question about elliptic modular forms with level, where results of Katz are
available. 相似文献
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Translated from Matematicheskie Zametki, Vol. 45, No. 3, pp. 101–107, March, 1989. 相似文献
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《Applied Mathematics Letters》2000,13(6):97-104
In this work, a new class of inverse Laplace transforms of exponential functions involving nested square roots are determined. Using these new inverses and other techniques from Laplace transform theory, a new class of three-parameter definite integrals, that yield to exact evaluation, is generated. It is shown that these integrals evaluate to simple closed-form expressions. These results are then verified using independent analytical techniques. Special and limiting cases of the parameters are investigated, some of which yield well-known expressions from classical analysis. Asymptotic results for these integrals and inverses are also given. In addition, a representation of the complementary error function as a limit is presented. Last, some aspects concerning the numerical implementation of these inverses are discussed and several applications in continuum mechanics are noted. 相似文献
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Tong Liu 《中国科学A辑(英文版)》1999,42(10):1009-1018
LetK
6 be a real cyclic sextic number field, andK
2,K
3 its quadratic and cubic subfield. Leth(L) denote the ideal class number of fieldL. Seven congruences forh
- =h (K
6)/(h(K
2)h(K
3)) are obtained. In particular, when the conductorf
6 ofK
6 is a primep,
, whereC is an explicitly given constant, andB
n is the Bernoulli number. These results on real cyclic sextic fields are an extension of the results on quadratic and cyclic
quartic fields.
Project supported by the National Natural Science Foundation of China (Grant No. 19771052). 相似文献
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In this paper a class of new inequalities about Bernstein polynomial is established. With these inequalities,the estimation of heights,the derivative bounds of Bézier curves and rational Bézier curves can be improved greatly. 相似文献
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For each sequence of positive real numbers,tending to positive infinity,a Furstenberg family is defined.All these Furstenberg families are compatible with dynamical systems.Then,chaos with respect to such Furstenberg families are intently discussed.This greatly improves some classical results of distributional chaos.To confirm the effectiveness of these improvements,the relevant examples are provided finally. 相似文献
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通过判断相关函数的Schur凸性、Schur几何凸性和Schur调和凸性,证明并推广了一类条件不等式,并据此建立了某些单形不等式. 相似文献
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给出了对称扩展的有界分配格的定义,即带有满足一定条件的一元运算的有界分配格.然后给出了这种分配格上的主同余的等式刻划及其可补性.最后,讨论了对称扩展的有界分配格的次直不可约性。 相似文献
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The Ramanujan Journal - An integral power series is called lacunary modulo M if almost all of its coefficients are divisible by M. Motivated by the parity problem for the partition function, Gordon... 相似文献
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We discuss a family of restricted m-ary overpartition functions bm,j (n), which is the number of m-ary overpartitions of n with at most i + j copies of the non-overlined part m^i allowed, and obtain a family of congruences for bm,lm-1 (n). 相似文献
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V.N. Phat 《Nonlinear Analysis: Theory, Methods & Applications》2009,71(12):6265-6275
The problem of Lyapunov stability for functional differential equations in Hilbert spaces is studied. The system to be considered is non-autonomous and the delay is time-varying. Known results on this problem are based on the Gronwall inequality yielding relative conservative bounds on nonlinear perturbations. In this paper, using more general Lyapunov-Krasovskii functional, neither model variable transformation nor bounding restriction on nonlinear perturbations is required to obtain improved conditions for the global exponential stability of the system. The conditions given in terms of the solution of standard Riccati differential equations allow to compute simultaneously the two bounds that characterize the stability rate of the solution. The proposed method can be easily applied to some control problems of nonlinear non-autonomous control time-delay systems. 相似文献
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In this paper, we study the existence and uniqueness of positive solutions for a class of nonlinear operator equations on ordered Banach spaces. Various applications are also considered to illustrate our obtained results (existence of solutions to quadratic integral equations with a linear modification of the argument, positive solution of second-order Neumann boundary value problem, and positive definite solutions of a class of nonlinear matrix equations). 相似文献
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D. Choi 《The Ramanujan Journal》2007,14(1):69-77
In this paper, we study the spaces of modular forms on Γ0(N) generated by eta-quotients, where the genus of Γ0(N) is zero or N is a prime. Our results give an answer to a question of Ono (2004, Problem 1.68).
2000 Mathematics Subject Classification Primary—11F20, 11F11 相似文献
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The Ramanujan Journal - Motivated by congruences for partitions, we study congruences for three well known arithmetic functions: the divisor function d(n), the sum-of-divisors function $$\sigma... 相似文献
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For x = (x 1, x 2, ..., x n ) ∈ ℝ+ n , the symmetric function ψ n (x, r) is defined by $\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } ,$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } , 相似文献