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, 2026

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

Key Points

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

Abstract

Abstract In this paper, we prove a lower bound result for extremely large values of L (12, 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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