What question did this study set out to answer?

To compute the mixed second moment of the derivatives of quadratic Dirichlet L-functions.

February 10, 2026Research in Number TheoryOpen Access

Moments of derivatives of quadratic Dirichlet L-functions with prime conductor

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To compute the mixed second moment of the derivatives of quadratic Dirichlet L-functions.
Calculated asymptotic formulas for the mixed second moment.
Analyzed the derivatives at specific orders of L-functions.
Focused on monic, irreducible polynomials in the function field.
Established a new asymptotic formula.
Characterized the behavior of derivatives of quadratic Dirichlet L-functions.
Found connections between derivatives and properties of the polynomials involved.

Implication

This research computes an asymptotic formula for mixed moments of derivatives of L-functions, suggesting new insights into number theory.

Abstract

We compute an asymptotic formula for the mixed second moment of the μ μ -th and ν ν -th derivatives of quadratic Dirichlet L -functions over monic, irreducible polynomials in the function field setting.

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Cite This Study

C. G. Best (2026) studied this question.

synapsesocial.com/papers/698acae37c832249c30ba829 https://doi.org/10.1007/s40993-026-00704-7

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Implication

This research computes an asymptotic formula for mixed moments of derivatives of L-functions, suggesting new insights into number theory.

Moments of derivatives of quadratic Dirichlet L-functions with prime conductor

Key Points

Implication

Abstract

Discussion

Cite This Study

Moments of derivatives of quadratic Dirichlet L-functions with prime conductor

Key Points

Implication

Abstract

Discussion

Cite This Study

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