共查询到20条相似文献,搜索用时 370 毫秒
1.
We characterize the function spanned by theta series. As an application we derive a simple proof of the modular identity of the theta series.
2.
We consider three-variable analogues of the theta series of Borwein and Borwein. We prove various identities involving these theta series including a generalization of the cubic identity of Borwein and Borwein. 相似文献
3.
Vignéras constructs non-holomorphic theta functions according to indefinite quadratic forms with arbitrary signature. We use
Vignéras’ theta functions to create examples of non-holomorphic Jacobi forms associated to indefinite theta series by two
different methods. 相似文献
4.
Josef F. Dorfmeister Sebastian Walcher 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2018,88(2):273-288
We discuss generalizations of classical theta series, requiring only some basic properties of the classical setting. As it turns out, the existence of a generalized theta transformation formula implies that the series is defined over a quasi-symmetric Siegel domain. In particular the exceptional symmetric tube domain does not admit a theta function. 相似文献
5.
H. Katsurada 《Journal of Number Theory》2004,104(1):100-117
We introduce a formula for the p-adic Siegel-Eisenstein series which demonstrates a connection with the genus theta series and the twisted Eisenstein series with level p. We then prove a generalization of Serre's formula in the elliptic modular case. 相似文献
6.
Hiro-aki Narita 《Mathematische Zeitschrift》2008,259(3):591-615
Tsuneo Arakawa formulated a theta lifting from elliptic cusp forms to automorphic forms on Sp(1,q) in his unpublished note, which was inspired by “Kudla lifting”, i.e. a theta lifting from elliptic modular forms to holomorphic
automorphic forms on SU(1,q). We prove that the images of Arakawa’s theta lifting belong to the space of bounded automorphic forms generating quaternionic
discrete series, which are non-holomorphic forms. In the appendix we provide the construction of Eisenstein series and Poincaré series generating such discrete series.
The author was partially supported by JSPS Research Fellowships for Young Scientist for April 2002 to March 2005. The results
of this paper were obtained in this period. 相似文献
7.
Y. Choie 《Journal of Mathematical Analysis and Applications》2007,325(2):1430-1441
In this paper we study linear relations among theta series of genera of positive definite n-ary quadratic forms with given level D,2D,4D and 8D for square free D. We obtain a basis for the space generated by genus theta series. This forms a basis of Eisenstein space. 相似文献
8.
Holly J. Rosson 《Journal of Number Theory》2002,94(1):49-79
Let K be the function field over a finite field of odd order, and let H be a definite quaternion algebra over K. If Λ is an order of level M in H, we define theta series for each ideal I of Λ using the reduced norm on H. Using harmonic analysis on the completed algebra H∞ and the arithmetic of quaternion algebras, we establish a transformation law for these theta series. We also define analogs of the classical Hecke operators and show that in general, the Hecke operators map the theta series to a linear combination of theta series attached to different ideals, a generalization of the classical Eichler Commutation Relation. 相似文献
9.
Mihnea Popa 《Transactions of the American Mathematical Society》2002,354(5):1869-1898
In this paper we approach the study of generalized theta linear series on moduli of vector bundles on curves via vector bundle techniques on abelian varieties.
We study a naturally defined class of vector bundles on a Jacobian, called Verlinde bundles, in order to obtain information about duality between theta functions and effective global and normal generation on these moduli spaces.
10.
Tonghai Yang 《Proceedings of the American Mathematical Society》1998,126(4):999-1004
In this note, we apply the method of Rodriguez Villegas and Yang (1996) to construct a family of infinite many theta series over the Hilbert-Blumenthal modular surfaces with a common zero. We also relate the non-vanishing of the central L-values of certain Hecke characters of non-biquadratic CM number fields of degree 4 to the nonvanishing of theta functions at CM points in the Hilbert-Blumenthal modular surfaces.
11.
Zhi-Guo Liu 《Journal of Number Theory》2012,132(12):2955-2966
In this paper we prove a theta function identity of degree eight using the theory of elliptic theta functions and the method of asymptotic analysis. This identity allows us to derive some curious Eisenstein series identities. We prove a new addition formula for theta functions which allows us to give an extension of the Hirschhorn septuple product identity. 相似文献
12.
Ramanujan studied the analytic properties of many q-hypergeometric series. Of those, mock theta functions have been particularly intriguing, and by work of Zwegers, we now know how these curious q-series fit into the theory of automorphic forms. The analytic theory of partial theta functions however, which have q-expansions resembling modular theta functions, is not well understood. Here we consider families of q-hypergeometric series which converge in two disjoint domains. In one domain, we show that these series are often equal to one another, and define mock theta functions, including the classical mock theta functions of Ramanujan, as well as certain combinatorial generating functions, as special cases. In the other domain, we prove that these series are typically not equal to one another, but instead are related by partial theta functions. 相似文献
13.
Zhi-Guo Liu 《Advances in Mathematics》2005,195(1):1-23
In this paper, we establish a three-term theta function identity using the complex variable theory of elliptic functions. This simple identity in form turns out to be quite useful and it is a common origin of many important theta function identities. From which the quintuple product identity and one general theta function identity related to the modular equations of the fifth order and many other interesting theta function identities are derived. We also give a new proof of the addition theorem for the Weierstrass elliptic function ℘. An identity involving the products of four theta functions is given and from which one theta function identity by McCullough and Shen is derived. The quintuple product identity is used to derive some Eisenstein series identities found in Ramanujan's lost notebook and our approach is different from that of Berndt and Yee. The proofs are self contained and elementary. 相似文献
14.
Kağan Kurşungöz 《The Ramanujan Journal》2017,43(1):95-112
We study unilateral series in a single variable q where its exponent is an unbounded increasing function and the coefficients are periodic. Such series converge inside the unit disk. Quadratic polynomials in the exponent correspond to partial theta series. We compute limits of those series as the variable tends radially to a root of unity. The proofs use ideas from the q-integral and are elementary. 相似文献
15.
We derive formulae for the theta series of the two translates of the even sublattice L0 of an odd unimodular lattice L that constitute the shadow of L. The proof rests on special evaluations of the Jacobi theta series attached to L and to a certain vector. We produce an analogous theorem for codes. Additionally, we construct non-linear formally self-dual codes and relate them to lattices. 相似文献
16.
Barquero-Sanchez Adrian Mantilla-Soler Guillermo Ryan Nathan C. 《The Ramanujan Journal》2021,56(2):613-630
The Ramanujan Journal - Let d and n be positive integers and let K be a totally real number field of discriminant d and degree n. We construct a theta series $$\theta _{K} \in {\mathcal... 相似文献
17.
We consider the action of suitable trace operators on non homogeneous theta series that are Siegel modular forms for the principal
congruence subgroups of the symplectic group of odd levelq: Г
n
[q]. This is used for investigating whether modular forms forГ
n
[N], withN|q, which are linear combination of such theta series, can be expressed as combination of theta series that are modular forms
with respect toГ
n
[N]. 相似文献
18.
Fu-Tsun Wei 《Mathematische Annalen》2013,355(1):235-258
We propose a concept of half integral weight in the global function field context, and construct natural families of functions with given weight. An analogue of Shimura correspondence (between weight 2 functions and weight ${\frac{3}{2}}$ functions) via theta series from “definite” quaternion algebras over function fields is then established. From the study of Fourier coefficients of these theta series, we arrive at a Waldspurger-type formula. This formula is then applied to L-series coming from elliptic curves over function fields. 相似文献
19.
Jacob Sturm 《Journal of Number Theory》1982,14(3):353-361
We show that a cusp form of weight , which corresponds to an Eisenstein series of weight 2 via the Shimura lifting, must be linear combination of theta series attached to quadratic forms of one variable. 相似文献
20.
Hiroshi Nozaki 《Archiv der Mathematik》2006,86(3):226-230
We prove that the theta series of any odd unimodular Euclidean lattice is not congruent to 1 modulo any odd prime p.
Received: 18 March 2005 相似文献