On the Ramanujan–Petersson conjecture for modular forms of half-integral weight
-
Sanoli Gun
and
Winfried Kohnen
Abstract
We investigate the (still unknown) Ramanujan–Petersson conjecture about the growth of the Fourier coefficients of cusp forms of half-integral weight and prove that it is optimal, at least for newforms in the plus space.
Acknowledgements
The authors would like to thank the referee for a very careful reading and relevant suggestions, which improved the presentation and clarity of the paper.
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Articles in the same Issue
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- Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics
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- Variable weak Hardy spaces WHLp(·)(ℝn) associated with operators satisfying Davies–Gaffney estimates
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- On the Ramanujan–Petersson conjecture for modular forms of half-integral weight
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Articles in the same Issue
- Frontmatter
- Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics
- Locally conformal symplectic structures on Lie algebras of type I and their solvmanifolds
- Variable weak Hardy spaces WHLp(·)(ℝn) associated with operators satisfying Davies–Gaffney estimates
- Sublinear operators on weighted Hardy spaces with variable exponents
- Hereditarily minimal topological groups
- Rational torsion of generalized Jacobians of modular and Drinfeld modular curves
- Morita homotopy theory for (∞,1)-categories and ∞-operads
- Homomorphisms into totally disconnected, locally compact groups with dense image
- On the Ramanujan–Petersson conjecture for modular forms of half-integral weight
- Uniform continuity of nonautonomous superposition operators in ΛBV-spaces
- Simple modules over the Lie algebras of divergence zero vector fields on a torus
- Effective bounds for the Andrews spt-function
- Free subgroups in k(x1,... ,xn)(X;σ) and k(x,y)(k;σ)
- A geometric proof of an equivariant Pieri rule for flag manifolds
- On relations between weak and strong type inequalities for modified maximal operators on non-doubling metric measure spaces
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Global well-posedness and temporal decay estimates to the fractional Cahn–Hilliard equation in
