共查询到20条相似文献,搜索用时 15 毫秒
1.
Hidekazu Tanaka 《The Ramanujan Journal》2012,28(3):409-422
We give a new proof of the modularity of the Dedekind eta function using a transformation formula of Stirling modular forms. Moreover, we study special values of multiple cotangent functions. Then we obtain some relations between special values of multiple cotangent functions. 相似文献
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Shin-ya Koyama 《Journal of Number Theory》2008,128(6):1769-1774
We construct the multiple Eisenstein series and we show a relation to the multiple cotangent function. We calculate a limit value of the multiple Eisenstein series. 相似文献
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Abdelmejid Bayad 《Integral Transforms and Special Functions》2018,29(8):611-622
We prove several relations on multiple Hurwitz–Riemann zeta functions. Using analytic continuation of these multiple Hurwitz–Riemann zeta functions, we quote at negative integers Euler's nonlinear relation for generalized Bernoulli polynomials and numbers. As an application, we give a general convolution identity for Bernoulli numbers. 相似文献
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Bai-Ni Guo Feng Qi 《International Journal of Mathematical Education in Science & Technology》2013,44(3):384-389
By using an identity relating to Bernoulli's numbers and power series expansions of cotangent function and logarithms of functions involving sine function, cosine function and tangent function, four inequalities involving cotangent function, sine function, secant function and tangent function are established. 相似文献
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关于亚纯函数的唯一性问题 总被引:7,自引:0,他引:7
本文应用 Nevanlinna理论研究亚纯函数的重值与唯一性问题,所得结果推广了某些已知的定理,并回答了C.C.Yang的一个猜测. 相似文献
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Theoretical investigations on maximal dual feasible functions 总被引:1,自引:0,他引:1
Dual feasible functions are used to get valid inequalities and lower bounds for integer linear problems. In this paper, we provide a simpler proof for maximality, and we describe new results concerning the extremality of functions from the literature. Extremal functions are a dominant class of dual feasible functions. 相似文献
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In this paper, we discuss the influence of multiple values and Valiron deficiencies on the uniqueness problem of algebroid functions on annuli, we get the several uniqueness theorems of algebroid functions on annuli, and also we extend the Nevanlinna value distribution theory for algebroid functions on annuli. 相似文献
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J. A. C. Weideman 《Numerische Mathematik》1992,61(1):409-432
Summary We derive expressions for the eigenvalues of spectral differentiation matrices for unbounded domains. In particular, we consider Galerkin and collocation methods based on Hermite functions as well as rational functions (a Fourier series combined with a cotangent mapping). We show that (i) first derivative matrices have purely imaginary eigenvalues and second derivative matrices have real and negative eigenvalues, (ii) for the Hermite method the eigenvalues are determined by the roots of the Hermite polynomials and for the rational method they are determined by the Laguerre polynomials, and (iii) the Hermite method has attractive stability properties in the sense of small condition numbers and spectral radii. 相似文献
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Kenro Furutani 《Annals of Global Analysis and Geometry》2002,22(1):1-27
We study a problem of the geometric quantization for the quaternionprojective space. First we explain a Kähler structure on the punctured cotangent bundleof the quaternion projective space, whose Kähler form coincides withthe natural symplectic form on the cotangent bundle and show thatthe canonical line bundle of this complex structure is holomorphicallytrivial by explicitly constructing a nowhere vanishing holomorphicglobal section. Then we construct a Hilbert space consisting of acertain class of holomorphic functions on the punctured cotangentbundle by the method ofpairing polarization and incidentally we construct an operatorfrom this Hilbert space to the L
2 space of the quaternionprojective space. Also we construct a similar operator between thesetwo Hilbert spaces through the Hopf fiberation.We prove that these operators quantizethe geodesic flow of the quaternion projective space tothe one parameter group of the unitary Fourier integral operatorsgenerated by the square root of the Laplacian plus suitable constant.Finally we remark that the Hilbert space above has the reproducing kernel. 相似文献
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Silvestru Sever Dragomir 《分析论及其应用》2023,39(1):1-15
In this paper, by making use of Divergence theorem for multiple integrals,
we establish some integral inequalities for Schur convex functions defined on bodies $B⊂\mathbb{R}^n$ that are symmetric, convex and have nonempty interiors. Examples for three
dimensional balls are also provided. 相似文献
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Ulrich Dieter 《Journal of Number Theory》1984,18(3):289-305
In this article a simple proof for a reciprocity formula for sums of cotangent functions is presented. If the second arguments are zero, these sums are four times the original Dedekind sums. Subsequently, explicit expressions are derived. Finally, it is shown that the Berndt sums are special cases of these sums. 相似文献
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Simona-Luiza Druţǎ-Romaniuc 《Czechoslovak Mathematical Journal》2012,62(4):937-949
We obtain the natural diagonal almost product and locally product structures on the total space of the cotangent bundle of a Riemannian manifold. Studying the compatibility and the anti-compatibility relations between the determined structures and a natural diagonal metric, we find the Riemannian almost product (locally product) and the (almost) para-Hermitian cotangent bundles of natural diagonal lift type. Finally, we prove the characterization theorem for the natural diagonal (almost) para-Kählerian structures on the total space of the cotangent bundle. 相似文献
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In this paper, we establish a decomposition theorem for polyharmonic functions and consider its applications to some Dirichlet problems in the unit disc. By the decomposition, we get the unique solution of the Dirichlet problem for polyharmonic functions (PHD problem) and give a unified expression for a class of kernel functions associated with the solution in the case of the unit disc introduced by Begehr, Du and Wang. In addition, we also discuss some quasi-Dirichlet problems for homogeneous mixed-partial differential equations of higher order. It is worthy to note that the decomposition theorem in the present paper is a natural extension of the Goursat decomposition theorem for biharmonic functions. 相似文献
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Nobushige Kurokawa 《Journal of Number Theory》2008,128(6):1775-1783
We show a limit formula for Eisenstein series by using the theory of a multiple cotangent function. The value is expressed simply via the Bernoulli number. 相似文献