Weighted spectral large sieve inequalities for Hecke congruence subgroups of \(\mathrm{SL}(2,\mathbb{Z}[i])\)

DOI10.7169/FACM/2013.48.2.4zbMath1277.11041arXiv1302.3127OpenAlexW3102889856MaRDI QIDQ351242

Nigel Watt

Publication date: 11 July 2013

Published in: Functiones et Approximatio. Commentarii Mathematici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.3127

zbMATH Keywords

spectral theoryKloosterman sumlarge sieveHecke charactermean valueGaussian integersautomorphic formcusp formFourier coefficienteigenvalue conjectureGaussian number fieldHecke congruence groupinverse Bessel transformnon-holomorphic modular form

Mathematics Subject Classification ID

Estimates on exponential sums (11L07) Asymptotic results on arithmetic functions (11N37) Other Dirichlet series and zeta functions (11M41) Gauss and Kloosterman sums; generalizations (11L05) Fourier coefficients of automorphic forms (11F30) Zeta functions and (L)-functions of number fields (11R42) Primes in congruence classes (11N13) Distribution of prime ideals (11R44) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72) Sieves (11N35)

Related Items (3)

Weighted spectral large sieve inequalities for Hecke congruence subgroups of \(\mathrm{SL}(2,\mathbb{Z}[i)\)] ⋮ Spectral large sieve inequalities for Hecke congruence subgroups of \(\mathrm{SL}(2,\mathbb{Z}[i)\)] ⋮ On the conformal spin dependence of the perturbative QCD vacuum singularity

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