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Tonghai Yang 《Transactions of the American Mathematical Society》2003,355(7):2663-2674
In this paper, we give an explicit formula for the first two terms of the Taylor expansion of a classical Eisenstein series of weight for . Both the first term and the second term have interesting arithmetic interpretations. We apply the result to compute the central derivative of some Hecke -functions.
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Let be a -adic field. It is well-known that has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions of a given degree and discriminant.
4.
Shamita Dutta Gupta Xiaotie She 《Proceedings of the American Mathematical Society》2000,128(8):2203-2212
In this paper, we obtain an Euler product with functional equation associated to a noncuspidal metaplectic form on the double cover of . Zagier's idea of Rankin-Selberg method is used to define the convolution of and the -function.
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We shall prove thatf
1 =x
2 +y
4 + 7z
2 represents all eligible numbers congruent to 2 mod 3 except 14 × 72k which was conjectured by Kanplansky. Our method is to use modular forms of weight 3/2. Our method can also be applied to
other ternary quadratic forms. 相似文献
6.
C. Mœglin 《Advances in Mathematics》2011,228(2):1068
This paper is about the pole of some Eisenstein series for classical groups over a number field. In a previous paper, we have shown how to normalize intertwining operators in such a way that they are holomorphic for positive parameters. Here we show that the image of such operators is (in the interesting cases) either 0 or an irreducible representation. This enables us to compute explicitly the residue of the Eisenstein series obtained from square integrable cohomological representations. At the end of the paper we give necessary and sufficient conditions in terms of Arthur?s data in order that a square integrable cohomological representation is cuspidal; the conditions are not totally satisfactory and we explain what we expect when Arthur?s results will be fully available. 相似文献
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本文在艾森斯坦因判别法的基础上,对整系数多项式的次高项系数进行了讨论,得到了整系数多项式在整数环上不可约的一个新的判别法。 相似文献
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Tsuyoshi Miezaki 《Journal of Pure and Applied Algebra》2019,223(10):4153-4160
Eisenstein polynomials, which were defined by Oura, are analogues of the concept of an Eisenstein series. Oura conjectured that there exist some analogous properties between Eisenstein series and Eisenstein polynomials. In this paper, we provide new analogous properties of Eisenstein polynomials and zeta polynomials. These properties are finite analogies of certain properties of Eisenstein series. 相似文献
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We introduce certain families of elliptic functions involving the Weierstrass ℘-function via q-series systematically and investigate their analytic and algebraic properties. Especially, we give examples of non-linear
algebraic ordinary differential equations satisfied by some such elliptic functions.
2000 Mathematics Subject Classification: Primary–11M36, 33E05 相似文献
10.
Yu. A. Pupyrev 《Mathematical Notes》2005,78(3-4):563-568
In the paper, results on linear and algebraic independence of q-series of the form $\varsigma _q (s) = \sum\nolimits_{n = 1}^\infty {\sigma _{s - 1} (n)q^n }$ over the field ?(q) are obtained, where $\sigma _{s - 1} (n) = \sum\nolimits_{d|n} {d^{s - 1} }$ , s = 1, 2,... . 相似文献