Results 11 to 20 of about 69,416 (237)
Coefficients of half-integral weight modular forms
Journal of Number Theory, 2003 Inspired by Kolyvagin's celebrated work on the Birch and Swinnerton-Dyer Conjecture and works of Waldspurger, Kohnen and Zagier relating the Fourier coefficients of half-integral weight Hecke eigenforms to values of modular \(L\)-functions (there have been a number of works on the indivisibility of the coefficients of half-integral weight modular forms)
Bruinier, Jan H., Ono, Ken
openaire +3 more sources
Nonzero coefficients of half-integral weight modular forms mod $$\ell $$ ℓ
Research in the Mathematical Sciences, 2018 Let \(K\) be a number field with ring of integers \(\mathcal{O}\). Let \(\ell\) be a prime number and \(\lambda\) a maximal ideal of \(\mathcal{O}\) above \(\ell\). Let \(f\) be a weakly holomorphic modular form of (non integral) half-integral weight and level \(\Gamma_1(N)\) for some integer \(N\geq 1\).
Bellaïche, J +2 more
openaire +5 more sources
Equidistribution of signs for Hilbert modular forms of half-integral weight
Research in Number Theory, 2018 We prove an equidistribution of signs for the Fourier coefficients of Hilbert modular forms of half-integral weight. Our study focuses on certain subfamilies of coefficients that are accessible via the Shimura correspondence.
Kaushik, Surjeet +2 more
core +3 more sources
Fourier coefficients of modular forms of half-integral weight
Mathematische Annalen, 1985 In two important papers [J. Math. Pures Appl., IX. Sér. 59, 1--32 (1980; Zbl 0412.10019); ibid. 60, 375--484 (1981; Zbl 0431.10015)] \textit{J.-L. Waldspurger} showed that under the Shimura correspondence between Hecke eigenforms of weight \(k+1/2\) and weight \(2k\) the square of the \(m\)th Fourier coefficient (\(m\) squarefree) of a form of half ...
openaire +5 more sources
Level lowering for half-integral weight modular forms [PDF]
Proceedings of the American Mathematical Society, 2010 In this paper we provide a level lowering result for half-integral weight modular forms. The main ingredients are the Shimura map from half-integral weight modular forms to integral weight modular forms along with a level lowering result for integral ...
Brown, Jim, Li, Yingkun
core +4 more sources
Fourier coefficients of modular forms of half-integral weight
Inventiones Mathematicae, 1987 The Fourier coefficients \(a_n\) of normalized cusp forms for \(\Gamma_0(4N)\) of half-integral weight \(k\geq 5/2\) are shown to satisfy for \(n\) square-free \[ a_ n=O(n^{k/2-2/7+\varepsilon}). \] This exponent is \(3/14\) more than the Ramanujan-Petersson conjecture would give.
openaire +4 more sources
Modular forms of half-integral weight on exceptional groups
Compositio MathematicaWe define a notion of modular forms of half-integral weight on the quaternionic exceptional groups. We prove that they have a well-behaved notion of Fourier coefficients, which are complex numbers defined up to multiplication by${\pm }1$. We analyze the minimal modular form$\Theta _{F_4}$on the double cover of$F_4$, following Loke–Savin and Ginzburg ...
Spencer Leslie, Aaron Pollack
openaire +5 more sources
Distinguished representations and modular forms of half-integral Weight
Inventiones Mathematicae, 1980 Piatetski-Shapiro, I.I., Gelbart, St.
openaire +3 more sources
On cycle integrals of weakly holomorphic modular forms [PDF]
, 2014 In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms.
Bringmann, Kathrin +2 more
core +3 more sources
Signs of Fourier coefficients of half-integral weight modular forms [PDF]
Mathematische Annalen, 2021 AbstractLet g be a Hecke cusp form of half-integral weight, level 4 and belonging to Kohnen’s plus subspace. Let c(n) denote the nth Fourier coefficient of g, normalized so that c(n) is real for all $$n \ge 1$$ n ≥ 1 .
Lester, Stephen +1 more
openaire +3 more sources