A problem concerning a character sum.

Teske, Edlyn; Williams, Hugh C.

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The spectrum of characters of ultrafilters on ω

Saharon Shelah (2008)

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We show the consistency of the statement: "the set of regular cardinals which are the characters of ultrafilters on ω is not convex". We also deal with the set of π-characters of ultrafilters on ω.

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[For the entire collection see Zbl 0742.00067.]In the first part some general results on Hecke algebras are recalled; the structure constants corresponding to the standard basis are defined; in the following the example of the commuting algebra of the Gelfand- Graev representation of the general linear group $G L (2, F)$ is examined; here $F$ is a finite field of $q$ elements; the structure constants are explicitly determined first for the standard basis and then for a new basis obtained via a Mellin-transformation....

A note on finite groups with few values in a column of the character table

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On the size of L(1,χ) and S. Chowla's hypothesis implying that L(1,χ) > 0 for s > 0 and for real characters χ

S. Louboutin (2013)

Colloquium Mathematicae

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We give explicit constants κ such that if χ is a real non-principal Dirichlet character for which L(1,χ) ≤ κ, then Chowla's hypothesis is not satisfied and we cannot use Chowla's method for proving that L(s,χ) > 0 for s > 0. These constants are larger than the previous ones κ = 1- log 2 = 0.306... and κ = 0.367... we obtained elsewhere.

Brauer-Kuroda relations for S-class numbers

Bart de Smit (2001)

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