What question did this study set out to answer?

To establish lower bounds for extremely large values of L(1/2,χ_p) for specific prime numbers.

February 8, 2026The Quarterly Journal of Mathematics

Extreme central values of quadratic Dirichlet L -functions with prime conductors

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To establish lower bounds for extremely large values of L(1/2,χ_p) for specific prime numbers.
Generalized the twisted first moment result of Baluyot–Pratt
Focused on short Dirichlet series
Examined primes with p congruent to 1 mod 8
Proved lower bound for L(1/2,χ_p) with prime p
Showed these bounds are significant for primes p in the specified residue class
Indicated the results can enhance understanding of Dirichlet series behavior

Implication

Research demonstrates lower bounds of L-values in primes, suggesting new insights into Dirichlet series.

Abstract

In this paper, we prove a lower bound result for extremely large values of L(1/2,χ ₚ) with prime numbers p≡ 1 8, based on generalizing the twisted first moment result of Baluyot–Pratt to the case of short Dirichlet series with large coefficients.

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Cite This Study

Fan et al. (2026) studied this question.

synapsesocial.com/papers/698828850fc35cd7a8848158 https://doi.org/10.1093/qmath/haag003

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Implication

Research demonstrates lower bounds of L-values in primes, suggesting new insights into Dirichlet series.

Extreme central values of quadratic Dirichlet L -functions with prime conductors

Key Points

Implication

Abstract

Discussion

Cite This Study

Extreme central values of quadratic Dirichlet L -functions with prime conductors

Key Points

Implication

Abstract

Discussion

Cite This Study

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