The distribution of values of L(1, χ d )

Granville, Andrew; Soundararajan, K.

doi:10.1007/s00039-003-0438-3

Cited by 130 publications

(215 citation statements)

References 13 publications

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“…8 Littlewood zeigte in [176], dass es unter Annahme der Richtigkeit der verallgemeinerten Riemannschen Vermutung unendlich viele quadratische Diskriminanten d gibt mit L (1, χ d ) ≥ (1 + o(1))e γ log log |d|. In [102] …”

Section: Danach Bemerkt Furtwängler Dass Die Kleinste Diskriminante unclassified

Der Briefwechsel Hasse - Scholz - Taussky

Hasse¹,

Scholz²,

Taussky³

2016

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Section: Danach Bemerkt Furtwängler Dass Die Kleinste Diskriminante unclassified

Der Briefwechsel Hasse - Scholz - Taussky

Hasse¹,

Scholz²,

Taussky³

2016

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“…Moreover the maximal size of character sums in an interval [x, x + y] is also determined up to a factor of 2. It is believed that the Ω result represents the true extreme values of L(1, χ) (see [8] for arguments in the case when χ is quadratic). Similarly we believe that (1.3) and (1.8) give the largest possible character sums.…”

Section: If G Is Even Thenmentioning

confidence: 99%

Large character sums: Pretentious characters and the Pólya-Vinogradov theorem

Granville¹,

Soundararajan

2006

J. Amer. Math. Soc.

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117

192

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In 1918 Pólya and Vinogradov gave an upper bound for the maximal size of character sums, which still remains the best known general estimate. One of the main results of this paper provides a substantial improvement of the Pólya-Vinogradov bound for characters of odd, bounded order. In 1977 Montgomery and Vaughan showed how the Pólya-Vinogradov inequality may be sharpened assuming the Generalized Riemann Hypothesis. We give a simple proof of their estimate and provide an improvement for characters of odd, bounded order. The paper also gives characterizations of the characters for which the maximal character sum is large, and it finds a hidden structure among these characters.

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“…In particular, they used the Cohen-Lenstra heuristics together with the work of Granville and Soundararajan [1] on the distribution of values of L(1, χ d ) to formulate a conjecture on the asymptotic nature of F (h) as h → ∞ through odd values. They also obtained the analogue of (1.1) for the average of hypothesis GRH.…”

Section: Introductionmentioning

confidence: 99%

“…Finally, using Proposition 1 of [1] (which states that the probability that L(1, X) ≤ π 2 /(6e γ τ ) is exp(−e τ −C 1 /τ (1 + o(1)) for some explicit constant C 1 ), we obtain…”

mentioning

confidence: 96%