共查询到20条相似文献,搜索用时 15 毫秒
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Yoshinori Mizuno 《Mathematische Zeitschrift》2012,272(3-4):1115-1135
We give meromorphic continuations and functional equations of Mellin transform and Rankin–Selberg convolution associated with a real analytic Eisenstein series of half-integral weight. Applications to Dirichlet series whose coefficients are the class numbers of binary quadratic forms are given. 相似文献
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A. B. Venkov 《Journal of Mathematical Sciences》1979,12(4):381-384
Starting from the Poincaré-Selberg series, another series is defined for a discrete group; the relationship is established between this series and the Dirichlet series for which the coefficients are products of the Fourier coefficients of the automorphic forms.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 63, pp. 3–7, 1976. 相似文献
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Koichi Takase 《manuscripta mathematica》1986,56(3):293-312
In this note, we will discuss the analogy of some results of Asai [2] in the case of the automorphic forms on SL(2,C). Being combined with the base change lifting to the imaginary quadratic field, we will discuss the L-function L(s,f,Sym2) for an elliptic modular form f. The base change lifting to the field of higher degree will also be discussed.The author would like to express his hearty thanks to Prof. Nobushige Kurokawa for his valuable suggestions on the meromorphy of Euler products. 相似文献
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One obtains theoretic-numerical results connected with the investigation of the Fourier coefficients of theta-series, associated with indefinite ternary quadratic forms.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 112, pp. 41–50, 1981. 相似文献
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The aim of this work is to analyze the structure of a tracially symmetric Dirichlet form on a -algebra, in terms of a killing weight and a closable derivation taking values in a Hilbert space with a bimodule structure. It is shown that the generator of the associate Markovian semigroup always appears, in a natural way, as the divergence of a closable derivation. Applications are shown to the decomposition of Dirichlet forms and to the construction of differential calculus on metric spaces. 相似文献
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V. G. Zhuravlev 《Journal of Mathematical Sciences》1982,18(3):350-373
The relation is studied between the behavior of Hilbert modular forms in a neighborhood of some manifold and the zeros on the critical line of the associated Dirichlet series. The results are applied to Eisenstein series associated with quadratic forms over real quadratic fields.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 76, pp. 89–123, 1978. 相似文献
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A Dirichlet series with multiplicative coefficients has an Euler product representation. In this paper we consider the special
case where these coefficients are derived from the numbers of representations of an integer by an integral quadratic form.
At first we suppose this quadratic form to be positive definite. In general the representation numbers are not multiplicative.
Instead we consider the average number of representations over all classes in the genus of the quadratic form. And we consider
only representations of integers of the form tk
2 with t square-free. If we divide the average representation number for these integers by a suitable factor, we do get a multiplicative
function. Using results from Siegel (Ann. Math. 36:527–606, 1935), we derive a uniform expression for the Euler product expansion of the corresponding Dirichlet series. As a special case,
we consider the standard quadratic form in n variables corresponding to the identity matrix. Here we use results from Shimura (Am. J. Math. 124:1059–1081, 2002). For 2≤n≤8, the genus of this particular quadratic form contains only one class, and this leads to a rather simple expression for
the Dirichlet series, where the coefficients are just the number of representations of a square as the sum of n squares. Finally we consider the indefinite case, where we can get results similar to the definite case. 相似文献
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We define a twisted two complex variables Rankin-Selberg convolution of Siegel cusp forms of degree 2. We find its group of
functional equations and prove its analytic continuation to . As an application we obtain a non-vanishing result for special values of the Fourier Jacobi coefficients. We also prove
the analytic properties for the characteristic twists of convolutions of Jacobi cusp forms.
Research Supported by Fondecyt grants 1061147, 7060241. 相似文献
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This paper deals with mean-value for the square of certain functionF(s) which has some characteristic properties of the Riemann zeta-function and its powers.Work supported by the University of the Basque Country. 相似文献
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We consider the possibility of the analytic continuation of the Dirichlet series SP;Z(s) associated with a polynomial P(x) and auxiliary series Z(s). In fact, we derive a certain criterion for the analytic continuation for some class of polynomials and give examples such that SP;Z(s) cannot be continued meromorphically to the whole plane C. We also study the asymptotic behaviors of the sum MP(x)=∑P(n1,…,nk)?xΛ(n1)?Λ(nk) considered first by M. Peter. Generalizations of this sum are also considered. 相似文献
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F. N. Garif’yanov 《Russian Mathematics (Iz VUZ)》2009,53(11):58-62
In this paper we consider Fuchsian groups of convergent type. We construct automorphic forms of various weights as lacunary
series with respect to a set of transformations of a group that does not have the structure of a subgroup. We also construct
an automorphic form of zero weight that is the Blaschke product. 相似文献
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Wladimir de Azevedo Pribitkin 《Journal of Number Theory》2011,131(11):2047-2060
We establish the oscillatory behavior of several significant classes of arithmetic functions that arise (at least presumably) in the study of automorphic forms. Specifically, we examine general L-functions conjectured to satisfy the Grand Riemann Hypothesis, Dirichlet series associated with classical entire forms of real weight and multiplier system, Rankin-Selberg convolutions (both “naive” and “modified”), and spinor zeta-functions of Hecke eigenforms on the Siegel modular group of genus two. For the second class we extend results obtained previously and jointly by M. Knopp, W. Kohnen, and the author, whereas for the fourth class we provide a new proof of a relatively recent result of W. Kohnen. 相似文献