Comparing Hecke eigenvalues of newforms
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DOI: 10.1007/s00013-017-1072-x
Abstract: Given two distinct newforms with real Fourier coefficients, we show that the set of primes where the Hecke eigenvalues of one of them dominate the Hecke eigenvalues of the other has density $$\ge $$≥1/16. Furthermore,… read more here.
Keywords: hecke eigenvalues; hecke; comparing hecke; eigenvalues newforms ... See more keywords
Asymptotics for Hecke eigenvalues of automorphic forms on compact arithmetic quotients
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DOI: 10.1016/j.aim.2022.108372
Abstract: In this paper, we describe the asymptotic distribution of Hecke eigenvalues in the Laplace eigenvalue aspect for certain families of Hecke-Maass forms on compact arithmetic quotients. In particular, we treat not only spherical, but also… read more here.
Keywords: compact arithmetic; hecke eigenvalues; asymptotics hecke; eigenvalues automorphic ... See more keywords
Congruences for Hecke eigenvalues in minus spaces
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DOI: 10.1016/j.jnt.2020.05.017
Abstract: Abstract The minus space M k ! − ( p ) is defined to be the subspace of the space M k ! ( p ) of weakly holomorphic weight k modular forms for Γ… read more here.
Keywords: congruences hecke; space; hecke eigenvalues; eigenvalues minus ... See more keywords
Random ordering in modulus of consecutive Hecke eigenvalues of primitive forms
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DOI: 10.1112/s0010437x18007455
Abstract: Let $\unicode[STIX]{x1D70F}(\cdot )$ be the classical Ramanujan $\unicode[STIX]{x1D70F}$ -function and let $k$ be a positive integer such that $\unicode[STIX]{x1D70F}(n)\neq 0$ for $1\leqslant n\leqslant k/2$ . (This is known to be true for $k read more here.
Keywords: hecke eigenvalues; stix x1d70e; unicode stix; stix x1d70f ... See more keywords
On Hecke eigenvalues of cusp forms in almost all short intervals
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DOI: 10.1142/s1793042122500385
Abstract: Let [Formula: see text] be a function such that [Formula: see text] as [Formula: see text]. Let [Formula: see text] be the [Formula: see text]th Hecke eigenvalue of a fixed holomorphic cusp form [Formula: see… read more here.
Keywords: eigenvalues cusp; hecke eigenvalues; see text; formula see ... See more keywords