The first moment of quadratic twists of modular $L$-functions

DOI10.4064/aa211207-7-11OpenAlexW4313477461MaRDI QIDQ5878049

Quanli Shen

Publication date: 17 February 2023

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2103.12284

zbMATH Keywords

recursive methodmoments of \(L\)-functionsmodular \(L\)-functions

Mathematics Subject Classification ID

(zeta (s)) and (L(s, chi)) (11M06) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67)

Cites Work

• Moments and distribution of central \(L\)-values of quadratic twists of elliptic curves
• The second moment of quadratic twists of modular \(L\)-functions
• Eisenstein series of \(1\over 2\)-integral weight and the mean value of real Dirichlet L-series
• Mean values of derivatives of modular \(L\)-series
• Determination of modular forms by twists of critical \(L\)-values
• Nonvanishing of quadratic Dirichlet \(L\)-functions at \(s=\frac{1}{2}\)
• The third moment of quadratic Dirichlet \(L\)-functions
• The analytic rank of \(J_0(q)\) and zeros of automorphic \(L\)-functions.
• Moments of quadratic twists of elliptic curve \(L\)-functions over function fields
• The second moment of quadratic Dirichlet \(L\)-functions
• Nonvanishing theorems for L-functions of modular forms and their derivatives
• Moments of L′(½) in the Family of Quadratic Twists
• A nonvanishing theorem for derivatives of automorphic 𝐿-functions with applications to elliptic curves
• The first moment of quadratic Dirichlet L-functions
• A mean value estimate for real character sums
• Conjectures and Experiments Concerning the Moments ofL(1/2, χ_d)
• Integral moments of L-functions
• On the order of vanishing of modular $L$-functions at the critical point
• Random matrix theory and \(L\)-functions at \(s=1/2\).

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