The Infona portal uses cookies, i.e. strings of text saved by a browser on the user's device. The portal can access those files and use them to remember the user's data, such as their chosen settings (screen view, interface language, etc.), or their login data. By using the Infona portal the user accepts automatic saving and using this information for portal operation purposes. More information on the subject can be found in the Privacy Policy and Terms of Service. By closing this window the user confirms that they have read the information on cookie usage, and they accept the privacy policy and the way cookies are used by the portal. You can change the cookie settings in your browser.
We are concerned here with Dirichlet series f(s)=1+∑n=2∞c(n)ns which satisfy a function equation similar to that of the Riemann zeta function, typically of the form f(s)=2sq1/2−sπs−1Γ(1−s)(sinπ2(s+κ))f(1−s), but for which the Riemann hypothesis is false. Indeed we show that the zeros of such functions are ubiquitous in the complex plane.
We study the degree of compactness of composition operators Cφ acting on weighted Hilbert spaces of entire functions, which include (i) the space of entire Dirichlet series, (ii) the space of entire power series, and (iii) the Fock space (we must have φ(z)=az+b, and it is known that Cφ is compact if and only if |a|<1). More precisely, the sequence (an) of approximation numbers of Cφ is investigated:...
Set the date range to filter the displayed results. You can set a starting date, ending date or both. You can enter the dates manually or choose them from the calendar.