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

MSC:
11R42 Zeta functions and \(L\)-functions of number fields
Citations:
Zbl 0744.11042
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References:
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[3] Haran, S.: Index theory, Potential Theory, and the Riemann hypothesis. In: Proc. LMS Symp. on ?L-functions and Arithmetic?, Durham, 1989 (to appear) · Zbl 0744.11042
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