A symbolic decision procedure for relations arising among Taylor coefficients of classical Jacobi theta functions

نویسنده

  • Liangjie Ye
چکیده

The class of objects we consider are algebraic relations between the four kinds of classical Jacobi theta functions θj(z|τ), j = 1, . . . , 4, and their derivatives. We present an algorithm to prove such relations automatically where the function argument z is zero, but where the parameter τ in the upper half complex plane is arbitrary.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Jacobi Theta Functions over Number Fields

We use Jacobi theta functions to construct examples of Jacobi forms over number fields. We determine the behavior under modular transformations by regarding certain coefficients of the Jacobi theta functions as specializations of symplectic theta functions. In addition, we show how sums of those Jacobi theta functions appear as a single coefficient of a symplectic theta function. 2000 Mathemati...

متن کامل

Exact Formulas for Coefficients of Jacobi Forms

In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...

متن کامل

Heun functions versus elliptic functions

We present some recent progresses on Heun functions, gathering results from classical analysis up to elliptic functions. We describe Picard’s generalization of Floquet’s theory for differential equations with doubly periodic coefficients and give the detailed forms of the level one Heun functions in terms of Jacobi theta functions. The finite-gap solutions give an interesting alternative integr...

متن کامل

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters

Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters Kathrin Bringmann,1,a) Amanda Folsom,2,b) and Antun Milas3,c) 1Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany 2Department of Mathematics and Statistics, Amherst College, Amherst, Massachusetts 01002, USA 3Department of Mathematics and Statistics, S...

متن کامل

Identification of Initial Taylor-Maclaurin Coefficients for Generalized Subclasses of Bi-Univalent Functions

In the present work, the author determines some coefficient bounds for functions in a new class of analytic and bi-univalent functions, which are introduced by using of polylogarithmic functions. The presented results in this paper one the generalization of the recent works of Srivastava et al. [26], Frasin and Aouf [13] and Siregar and Darus [25].

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • J. Symb. Comput.

دوره 82  شماره 

صفحات  -

تاریخ انتشار 2017