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Period ratios of modular forms

Mathematische Annalen, 2000
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Periods of automorphic forms

2012
In this chapter we introduce various notions connected to periods of automorphic forms; all of these have received extensive treatment in Shimura’s work. The period conjectures of Shimura occupy a central position in number theory today, and will be discussed in more detail in Chapter 3 and Chapter 6.
Ze-Li Dou, Qiao Zhang
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Forms of the Periodic Table

2019
A good deal has been said about the periodic table in previous chapters, but one important aspect has not yet been addressed. This is the question of why so many different periodic tables have been published in textbooks, articles, and on the Internet. One may also wonder whether there exists an “optimal periodic table” and whether such a question even
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Periods of Modular Forms

1982
In this chapter we develop the tools needed to describe the subgroup of H1(X(Γ);ℚ/ℤ) corresponding to the cuspidal group C(Γ).
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PERIODS OF AUTOMORPHIC FORMS: THE TRILINEAR CASE

Journal of the Institute of Mathematics of Jussieu, 2015
Following Jacquet, Lapid and Rogawski, we regularize trilinear periods. We use the regularized trilinear periods to compute Fourier–Jacobi periods of residues of Eisenstein series on metaplectic groups, which has an application to the Gan–Gross–Prasad conjecture.
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Half integral weight Jacobi forms and periods¶of modular forms

manuscripta mathematica, 2001
In [Abh. Math. Semin. Univ. Hamb. 16, 1-28 (1949; Zbl 0035.06004)], \textit{G. Bol} proved: Suppose \(r\in \mathbb{Z}\), \(r\geq 0\); then \[ D^{(r+1)} \Biggl\{(c\tau+d)^r F\biggl( \frac{a\tau+b}{c\tau+d} \biggr)\Biggr\}= (c\tau+d)^{-r-2} F^{(r+1)} \biggl( \frac{a\tau+b}{c\tau+d} \biggr), \] for \(ad-bc=1\) and any \(F\) defined on the complex plane \(\
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