Results 211 to 220 of about 167,831,130 (242)

ON THE FOURIER COEFFICIENTS OF MODULAR FORMS OF HALF-INTEGRAL WEIGHT

International Journal of Number Theory, 2013
It is known that if the Fourier coefficients a(n)(n ≥ 1) of an elliptic modular form of even integral weight k ≥ 2 on the Hecke congruence subgroup Γ0(N)(N ∈ N) satisfy the bound a(n) ≪f nc for all n ≥ 1, where c > 0 is any number strictly less than k - 1, then f must be cuspidal.
Choie, YJ, Kohnen, W
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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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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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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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On Jacobi forms and Siegel modular forms of half integral weights

Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1992
The author gives an explicit Hecke-equivariant isomorphism on the level of Fourier coefficients between the space of Jacobi forms of even integral weight \(k\) and index 1 w.r.t. \(\text{Sp}_ n(\mathbb{Z})\) and a certain subspace of Siegel modular forms of half-integral weight \(k-1/2\) w.r.t. the subgroup \(\Gamma_ 0(4) \subset \text{Sp}_ n(\mathbb{Z}
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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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A canonical subspace of modular forms of half-integral weight

Mathematische Annalen, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Gun, Sanoli, Manickam, M., Ramakrishnan, B.   +2 more
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Hecke operators on modular forms of half-integral weight

Archiv der Mathematik, 1988
In the paper [Arch. Math. 32, 158-165 (1979; Zbl 0407.10022)] \textit{Hong- Jen Hsiao} and \textit{Hong-Chang Lee} have proved that the Dirichlet series associated with a modular form f of integral weight for the full modular group has an Euler product expansion if and only if f is an eigenfunction for finitely many explicitly given Hecke operators. In
Manickam, M., Ramakrishnan, B., Vasudevan, T. C.   +2 more
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On the Shintani lifting of integral weight modular forms to half-integral weight modular forms

International Journal of Number Theory
In this paper, we explore the adelic Shintani lifting of a weight 2 cusp form f. For a finite Schwartz function related to an auxiliary quadratic character [Formula: see text], we express certain Fourier coefficients of this lifting in terms of the twisted L-value [Formula: see text].
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