Results 151 to 160 of about 687,398 (165)

Half-integral Weight Forms

2019
A Shimura correspondence is a Hecke equivariant map from half-integral to integral weight modular forms, and a Shintani lifting provides a similar map from integral to half-integral weight forms. In this chapter we extend the notion of quasimodular and Jacobi-like forms to the cases of half-integral weights and study quasimodular analogs of the Shimura
YoungJu Choie, Min Ho Lee
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On modular forms of half integral weight

The Annals of Mathematics, 1973
The recent development of the theory of modular forms and associated zeta functions, together with all its arithmetic significance, is quite pleasing, and our knowledge in this field is evergrowing, but the forms of half integral weight have attracted only casual attention, in spite of their importance and ancientness.
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Modular Forms of Half Integral Weight

2006
The forms to be discussed are those with the automorphic factor (cz + d)k/2 with a positive odd integer k. The theta function $$ \theta \left( z \right) = \sum\nolimits_{n = - \infty }^\infty {e^{2\pi in^2 z} } $$ and the Dedekind eta function $$ \eta \left( z \right) = e^{\pi iz/12} \prod _{n = 1}^\infty (1 - e^{2\pi inz} ) $$ are ...
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Modular Forms with Integral Weight or Half-integral Weight

2012
Let Г be a Fuchsian group of the first kind. Then M = Г ∖ ℍ* is a compact Riemann surface. Denote by K the field of all meromorphic functions on M. It is well-known that K is an algebraic function field over ℂ Let ϕ: ℍ*→ M be the natural map. For g ∈ K we call f(z) = g(ϕ(z)) an automorphic function on ℍ which is a meromorphic function on ℍ. It is clear
Xueli Wang, Dingyi Pei
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Coefficients of half-integral weight modular forms modulo ?j

Mathematische Annalen, 2004
For a half-integral weight cusp form \(F(z)\) with Fourier series \[ \sum_{n \geq 1} a(n)q^n, \] where the \(a(n)\) are integers, the authors say that the coefficients \(a(n)\) are \textit{well-distributed} modulo \(M\) if for every integer \(r\), \[ \#\{ 1 \leq n \leq X : a(n) \equiv r \pmod{M} \} \gg_{r,M} \begin{cases} \frac{\sqrt{X}}{\log X ...
Ahlgren, Scott, Boylan, Matthew
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On Fourier coefficients of half-integral weight modular forms

2017
In this talk, we give an exposition on some recent work, due to various researchers, on the sign of the Fourier coefficients of modular forms when the Fourier coefficients are real. Our main concern is the case of half-integral weight, and we shall discuss an interesting application due to Ben Kane.
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