The Chebotarev density theorem in short intervals and some questions of Serre

DOI10.1006/jnth.2001.2694zbMath1016.11053OpenAlexW2059554072MaRDI QIDQ5960971

Antal Balog, Ken Ono

Publication date: 22 April 2002

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/b33e9cccc415f88fca14357b8f066ddd691e3677

zbMATH Keywords

elliptic curverankcusp formChebotarev density theoremhalf-integer weightnonzero coefficientshort-interval

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Forms of half-integer weight; nonholomorphic modular forms (11F37) Holomorphic modular forms of integral weight (11F11) Density theorems (11R45)

Related Items (23)

ON THE DISTRIBUTION OF -FREE NUMBERS AND NON-VANISHING FOURIER COEFFICIENTS OF CUSP FORMS ⋮ The Sato–Tate Distribution and the Values of Fourier Coefficients of Modular Newforms ⋮ Nonvanishing of Fourier coefficients of modular forms ⋮ ON FUNDAMENTAL FOURIER COEFFICIENTS OF SIEGEL MODULAR FORMS ⋮ On squares in polynomial products ⋮ Gaps between nonzero Fourier coefficients of cusp forms ⋮ NONVANISHING OF THE RAMANUJAN TAU FUNCTION IN SHORT INTERVALS ⋮ AVERAGE SIZE OF GAPS IN THE FOURIER EXPANSION OF MODULAR FORMS ⋮ On the gaps between nonzero Fourier coefficients of eigenforms with CM ⋮ Primes in short intervals on curves over finite fields ⋮ On the gaps between non-zero Fourier coefficients of cusp forms of higher weight ⋮ A variant of the Bombieri–Vinogradov theorem in short intervals and some questions of Serre ⋮ On the gaps in the Fourier expansion of cusp forms ⋮ Cyclicity and exponents of CM elliptic curves modulo $p$ in short intervals ⋮ The first simultaneous sign change and non-vanishing of Hecke eigenvalues of newforms ⋮ Diophantine approximation with mild divisibility constraints ⋮ A note on small gaps between nonzero Fourier coefficients of cusp forms ⋮ Small gaps in coefficients of \(L\)-functions and \({\mathfrak B}\)-free numbers in short intervals ⋮ Chebotarev density theorem in short intervals for extensions of 𝔽_{𝕢}(𝕋) ⋮ The number of Hecke eigenvalues of same signs ⋮ On quasimodular eigenforms ⋮ Counting problems for geodesics on arithmetic hyperbolic surfaces ⋮ On Fourier coefficients of elliptic modular forms \(\bmod\ell\) with applications to Siegel modular forms

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