Functional Equation for Theta Series
نویسنده
چکیده
In this short paper, we find the transformation formula for the theta series under the action of the Jacobi modular group on the Siegel-Jacobi space. This formula generalizes the formula (5.1) obtained by Mumford in [3, p. 189].
منابع مشابه
Riemann ’ s and ζ ( s )
[This document is http://www.math.umn.edu/ ̃garrett/m/complex/notes 2014-15/09c Riemann and zeta.pdf] 1. Riemann’s explicit formula 2. Analytic continuation and functional equation of ζ(s) 3. Appendix: Perron identity [Riemann 1859] exhibited a precise relationship between primes and zeros of ζ(s). A similar idea applies to any zeta or L-function with analytic continuation, functional equation, ...
متن کاملTheta Functionswith Harmonic Coe⁄cients over Number Fields
is a modular form of weight n=2þ n on G0ðN Þ, where G 1⁄4 SL2ðZÞ and N is the level of Q, i.e., NQ 1 is integral and NQ 1 has even diagonal entries. This was proved by Schoeneberg [13] for even n and by Pfetzer [9] for odd n. Shimura [14] generalizes their results for arbitrary n and also computes the theta multiplier explicitly. Andrianov and Maloletkin [1, 2] generalize (1) and define theta s...
متن کاملOn the L - Function
Let CA/Q be the curve y = x + A, and let L(s, JA) denote the L-series of its Jacobian. Under the assumption that the sign in the functional equation for L(s, JA) is +1, we evaluate the critical value L(1, JA) in terms of the value of a theta series for Q( √ 5) depending on A at a CM point coming from Q(ζ5).
متن کاملOn the L-function of the Curves
Let CA/Q be the curve y = x + A, and let L(s, JA) denote the L-series of its Jacobian. Under the assumption that the sign in the functional equation for L(s, JA) is +1, we evaluate the critical value L(1, JA) in terms of the value of a theta series for Q( √ 5) depending on A at a CM point coming from Q(ζ5).
متن کاملFourier coefficients of sextic theta series
This article focuses on the theta series on the 6-fold cover of GL2. We investigate the Fourier coefficients τ(r) of the theta series, and give partially proven, partially conjectured values for τ(π)2, τ(π2) and τ(π4) for prime values π.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2008