A modified CFKRS recipe correctly predicts the secondary main term in the second moment of Dirichlet L-functions along cosets by incorporating the non-independence of root numbers and coefficients.
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Any number of primitive GL(1) and GL(2) L-functions can simultaneously take large values on the critical line unconditionally, improving prior conditional results.
Upper bounds on the least prime satisfying the Ramanujan conjecture simultaneously for two or three Hecke-Maass forms, and lower bounds on the natural density of primes satisfying it for at least one form in a given set.
citing papers explorer
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Remarks on the distribution of Dirichlet $L$-functions along cosets
A modified CFKRS recipe correctly predicts the secondary main term in the second moment of Dirichlet L-functions along cosets by incorporating the non-independence of root numbers and coefficients.
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Joint extreme values of $L$-functions on and off the critical line
Any number of primitive GL(1) and GL(2) L-functions can simultaneously take large values on the critical line unconditionally, improving prior conditional results.
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On Ramanujan Primes for Hecke-Maass Cusp Forms
Upper bounds on the least prime satisfying the Ramanujan conjecture simultaneously for two or three Hecke-Maass forms, and lower bounds on the natural density of primes satisfying it for at least one form in a given set.