On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms
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Sunil L. Naik
Abstract
In this article, we derive lower bounds for the number of distinct prime divisors of families of non-zero Fourier coefficients of non-CM primitive cusp forms and more generally of non-CM primitive Hilbert cusp forms.
In particular, for the Ramanujan Δ-function, we show that, for any
distinct prime factors for almost all primes 𝑝. This improves and refines the existing bounds. We also study lower bounds for absolute norms of radicals of non-zero Fourier coefficients of modular forms alluded to above.
Acknowledgements
The author would like to thank Sanoli Gun and Purusottam Rath for their support and guidance. The author would also like to thank the referee for helpful suggestions. The author would also like to acknowledge the support of DAE number theory plan project.
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Communicated by: Jan Bruinier
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- The Stiefel–Whitney classes of moment-angle manifolds are trivial
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- Construction of a class of spectral measures
- On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms
- Molecular characterization of weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type with its applications to Littlewood–Paley function characterizations
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Articles in the same Issue
- Frontmatter
- Wong–Zakai approximations and support theorems for stochastic McKean–Vlasov equations
- The Singer transfer for infinite real projective space
- The Stiefel–Whitney classes of moment-angle manifolds are trivial
-
On almost p-rational characters of
- Homogeneous four-manifolds with half-harmonic Weyl curvature tensor
- Construction of a class of spectral measures
- On the number of prime divisors and radicals of non-zero Fourier coefficients of Hilbert cusp forms
- Molecular characterization of weak Hardy spaces associated with ball quasi-Banach function spaces on spaces of homogeneous type with its applications to Littlewood–Paley function characterizations
- Conway invariant Jacobi forms on the Leech lattice
- Geometric characterizations of Gromov hyperbolic Hölder domains
- Improved quantitative unique continuation for complex-valued drift equations in the plane
- On uniqueness of branching to fixed point Lie subalgebras
- Fefferman type criterion on weighted bi-parameter local Hardy spaces and boundedness of bi-parameter pseudodifferential operators
