A sequential Riesz-like criterion for the Riemann Hypothesis.
A simple proof of the mean fourth power estimate for and
A simplification of the formula for L(1,χ) where χ is a totally imaginary Dirichlet character of a real quadratic field
A singular series average and Goldbach numbers in short intervals
A spectral analysis of automorphic distributions and Poisson summation formulas
Automorphic distributions are distributions on , invariant under the linear action of the group . Combs are characterized by the additional requirement of being measures supported in : their decomposition into homogeneous components involves the family , of Eisenstein distributions, and the coefficients of the decomposition are given as Dirichlet series . Functional equations of the usual (Hecke) kind relative to turn out to be equivalent to the invariance of the comb under some modification...
A statistical density theorem for L-functions with applications
A strategy for proving Riemann hypothesis.
A strengthening of the Nyman-Beurling criterion for the Riemann hypothesis
According to the well-known Nyman-Beurling criterion the Riemann hypothesis is equivalent to the possibility of approximating the characteristic function of the interval in mean square norm by linear combinations of the dilations of the fractional parts for real greater than . It was conjectured and established here that the statement remains true if the dilations are restricted to those where the ’s are positive integers. A constructive sequence of such approximations is given.
A study of the mean value of the error term in the mean square formula of the Riemann zeta-function in the critical strip
Let be the error term in the mean square formula of the Riemann zeta-function in the critical strip . It is an analogue of the classical error term . The research of has a long history but the investigation of is quite new. In particular there is only a few information known about for . As an exploration, we study its mean value . In this paper, we give it an Atkinson-type series expansion and explore many of its properties as a function of .
A subconvexity bound for Hecke L-functions
A Tauberian theorem for the Ingham summation method
A variant of Selberg's asymptotic formula.
A zero density result for the Riemann zeta function
We prove an explicit bound for N(σ,T), the number of zeros of the Riemann zeta function satisfying ℜ𝔢 s ≥ σ and 0 ≤ ℑ𝔪 s ≤ T. This result provides a significant improvement to Rosser's bound for N(T) when used for estimating prime counting functions.
A χ-analogue of a formula of Ramanujan for ζ(1/2)
Absolute derivations and zeta functions.
Absolute tensor products, Kummer's formula and functional equations for multiple Hurwitz zeta functions
Abundant numbers and the Riemann hypothesis.
Addendum to “On the problem”
Addendum to the paper " On the zeros of a class of generalized Dirichlet series".
Addition of : application to arithmetic.