1987 | OriginalPaper | Buchkapitel
Applications of Guinand’s Formula
verfasst von : P. X. Gallagher
Erschienen in: Analytic Number Theory and Diophantine Problems
Verlag: Birkhäuser Boston
Enthalten in: Professional Book Archive
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The explicit formula of Weil [21] connects quite general sums over primes with corresponding sums over the critical zeros of the Riemann zeta function (or more general L-functions). In the earlier version of Guinand [8], there is on the Riemann hypothesis1) a kind of Fourier duality between the differentials of the remainder terms in the prime number theorem (suitable renormalized) and in the formula counting critical zeros of the Riemann zeta function.