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Showing 1 to 6 of 6 for “"generalized riemann hypothesis"”.
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Counterexamples related to the Sato-Tate conjecture
… statistic. This conjecture implies the Riemann hypothesis for all $L$-functions associated with $E$. It is natural to assume that the converse (``generalized Riemann hypothesis implies discrepancy estimate'') holds, as is suggested by analogy with Artin $L$-functions. We construct, for …
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THE EFFECTIVE SATO-TATE CONJECTURE AND DENSITIES PERTAINING TO LEHMER-TYPE QUESTIONS
… of f(z) are automorphic and satisfy the Generalized Riemann Hypothesis. We use this result to compute the density of positive integers n for which the n-th Fourier coefficient of f(z) is nonzero.
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Zeros of the Dedekind Zeta-Function
… sums over two sets of nontrivial zeros of the Riemann zeta-function. Assuming the Riemann Hypothesis, he used this formula and Fourier analysis to prove an estimate for the proportion of simple zeros of the Riemann zeta-function. We prove a generalization of his formula for the nontrivial zeros …
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On the Theory of Zeta-functions and L-functions
… we provide a body of knowledge that concerns Riemann zeta-function and its generalizations in a cohesive manner. In particular, we have studied and mentioned some recent results regarding Hurwitz and Lerch functions, as well as Dirichlet's L-function. We have also investigated some fundamental …
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Moments Of Products Of L-Functions
… times the average spacing. Finally, assuming the Generalized Riemann Hypothesis and some standard conjectures, we prove upper bounds for moments of arbitrary products of automorphic L-functions and for Dedekind zeta-functions of Galois number fields on the critical line. As an application, we use …
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Topics in Multiplicative and Probabilistic Number Theory
… both unconditionally and assuming the Generalized Riemann Hypothesis, and show that our conditional results are nearly best possible unconditionally. We also prove a quantitative bivariate Erdo&huml;s-Kac theorem on the joint distribution of pairs of values of certain additive …