Neue Anwendungen der Theorie der Diophantischen Approximationen auf die Riemannsche Zetafunktion.
New formulations of the class number one problem
New inequalities involving the zeta function.
New integral representations for the square of the Riemann zeta-function
Introduction. The recent discovery of an analogue of the Riemann-Siegel integral formula for Dirichlet series associated with cusp forms [2] naturally raises the question whether similar formulas might exist for other types of zeta functions. The proof of these formulas depends on the functional equation for the underlying Dirichlet series. In both cases, for ζ(s) and for the cusp form zeta functions, only a simple gamma factor is involved. The next simplest case arises when two such factors occur...
New series involving the zeta function.
Note on a Paper by h. l. Montgomery ``omega Theorems for the Riemann Zeta-function''
Note on Dirichlet's L-functions
Note on some greatest common divisor matrices
Some quadratic forms related to "greatest common divisor matrices" are represented in terms of L²-norms of rather simple functions. Our formula is especially useful when the size of the matrix grows, and we will study the asymptotic behaviour of the smallest and largest eigenvalues. Indeed, a sharp bound in terms of the zeta function is obtained. Our leading example is a hybrid between Hilbert's matrix and Smith's matrix.
Note sur la série
Notes on the Riemann zeta-function, II