Mean values of derivatives of \(L\)-functions in function fields. I.

DOI10.1016/J.JMAA.2016.05.019zbMath1412.11116OpenAlexW2407633420WikidataQ57937381 ScholiaQ57937381MaRDI QIDQ298144

Surajit Rajagopal, Julio C. Andrade

Publication date: 20 June 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.05.019

zbMATH Keywords

function fieldshyperelliptic curvesrandom matrix theoryderivatives of \(L\)-functionsmoments of \(L\)-functionsquadratic Dirichlet \(L\)-functions

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Other Dirichlet series and zeta functions (11M41)

Related Items (9)

The mixed second moment of quadratic Dirichlet \(L\)-functions over function fields ⋮ Mean values of derivatives of \(L\)-functions in function fields. II. ⋮ Note on the mean values of derivatives of quadratic Dirichlet \(L\)-functions in function fields ⋮ Unnamed Item ⋮ Mean values of derivatives of L-functions in function fields: III ⋮ Mean values of derivatives of $L$-functions in function fields: IV ⋮ Unnamed Item ⋮ The first moment of $L\bigl(\frac{1}{2},\chi\bigr)$ for real quadratic function fields ⋮ Mean values of derivatives of \(L\)-functions for cyclotomic characters in function fields

Cites Work

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• The mean value of \(L(\frac{1}{2}, \chi)\) in the hyperelliptic ensemble
• Mean values of the Riemann zeta-function and its derivatives
• Rudnick and Soundararajan's theorem for function fields
• Note on the mean value of \(L(\tfrac 12,\chi )\) in the hyperelliptic ensemble
• Moments of the derivative of characteristic polynomials with an application to the Riemann zeta function
• A simple proof of the mean value of \(|K_2(\mathcal O)|\) in function fields
• Statistics of the zeros of zeta functions in families of hyperelliptic curves over a finite field
• THE FOURTH MOMENT OF DERIVATIVES OF THE RIEMANN ZETA-FUNCTION
• Average values of L-series in function fields.

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