Riesz potentials and explicit sums in arithmetic. (English) Zbl 0788.11055

Haran, Shai

Invent. Math. 101, No. 3, 697-703 (1990).

The paper originates with Weil’s formulas relating zeros of zeta functions of number fields and the distribution of prime ideals. This is shown to be connected with adelic Riesz potentials. For the motivation behind the paper, the reader is referred to S. Haran [Proc. Symp., Durham 1989, Lond. Math. Soc. Lect. Notes Ser. 153, 257-270 (1991; Zbl 0744.11042)]. The paper gives a finite expression for the contribution at infinity and a uniform way of expressing the contribution for a finite and infinite prime.

Reviewer: A.A.Terras (La Jolla)

MSC:

11R42

Zeta functions and \(L\)-functions of number fields

Keywords:

Weil explicit formulas; zeros of zeta functions; distribution of prime ideals; adelic Riesz potentials

Citations:

Zbl 0744.11042

References:

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