The ratios conjecture for real Dirichlet characters and multiple Dirichlet series

DOI10.1090/TRAN/9113MaRDI QIDQ6567170

Martin Čech

Publication date: 4 July 2024

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

functional equationmultiple Dirichlet seriesDirichlet \(L\)-functionsDirichlet charactersratios conjecture

Mathematics Subject Classification ID

Nonreal zeros of (zeta (s)) and (L(s, chi)); Riemann and other hypotheses (11M26) Multiple Dirichlet series and zeta functions and multizeta values (11M32)

Cites Work

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• An elliptic curve test of the \(L\)-functions ratios conjecture
• One-level density of families of elliptic curves and the Ratios Conjecture
• A unitary test of the Ratios Conjecture
• Autocorrelation of ratios of \(L\)-functions
• Eisenstein series of \(1\over 2\)-integral weight and the mean value of real Dirichlet L-series
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• Surpassing the ratios conjecture in the 1-level density of Dirichlet \(L\)-functions
• Type-I contributions to the one and two level densities of quadratic Dirichlet \(L\)-functions over function fields
• A theorem on analytic continuation of functions in several variables.
• Subconvexity for a double Dirichlet series
• An orthogonal test of the L-functions Ratios Conjecture, II
• Long mollifiers of the Riemann Zeta‐function
• An orthogonal test of the L -functions Ratios conjecture
• A Symplectic Test of the L-Functions Ratios Conjecture
• Zeroes of zeta functions and symmetry
• Multiple Dirichlet Series and Moments of Zeta and L-Functions
• On the distribution of the nontrivial zeros of quadratic L-functions close to the real axis
• On some applications of automorphic forms to number theory
• Introduction: Multiple Dirichlet Series
• Applications of theL-functions ratios conjectures
• Integral moments of L-functions
• The Ratios Conjecture and upper bounds for negative moments of 𝐿-functions over function fields

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