On the second moment for primes in an arithmetic progression
On the stationary points of Hardy's function Z(t)
On the success and failure of Gram's Law and the Rosser Rule
Opět o Riemannově dzeta funkci
Oscillation of Mertens’ product formula
Mertens’ product formula asserts thatas . Calculation shows that the right side of the formula exceeds the left side for . It was suggested by Rosser and Schoenfeld that, by analogy with Littlewood’s result on , this and a complementary inequality might change their sense for sufficiently large values of . We show this to be the case.
Pair correlation of the zeros of the Riemann zeta function in longer ranges
Polynomial interpolation and asymptotic representations for zeta functions [Book]
Primes in almost all short intervals. II
In questo lavoro vengono migliorati i risultati ottenuti in «Primes in Almost All Short Intervals» riguardo la distribuzione dei primi in quasi tutti gli intervalli corti della forma , con funzione reale appartenente ad una ampia classe di funzioni. Il problema viene trattato mettendo in relazione l'insieme eccezionale per la distribuzione dei primi in intervalli nella forma con l'insieme eccezionale per la formula asintotica I risultati presentati vengono quindi ottenuti grazie allo studio...
Primes with preassigned digits
Primitive lattice points in convex planar domains
Příspěvek ke vztahu Fareyovy řady a Riemannovy domněnky
Remarks on Weil’s quadratic functional in the theory of prime numbers, I
This Memoir studies Weil’s well-known Explicit Formula in the theory of prime numbers and its associated quadratic functional, which is positive semidefinite if and only if the Riemann Hypothesis is true. We prove that this quadratic functional attains its minimum in the unit ball of the -space of functions with support in a given interval , and prove again Yoshida’s theorem that it is positive definite if is sufficiently small. The Fourier transform of the functional gives rise to a quadratic...
Repulsive behavior in an exceptional family
Results on the distribution of primes.
Riemann's Hypothesis
Riemann’s memoir is devoted to the function π(x) defined as the number of prime numbers less or equal to the real and positive number x. This is really the fact, but the “main role” in it is played by the already mentioned zeta-function.
Small gaps between zeros of twisted L-functions
Small prime solutions of linear ternary equations
Small values of the Euler function and the Riemann hypothesis
Some conjectures on the zeros of approximates to the Riemann ≡-function and incomplete gamma functions
Riemann conjectured that all the zeros of the Riemann ≡-function are real, which is now known as the Riemann Hypothesis (RH). In this article we introduce the study of the zeros of the truncated sums ≡N(z) in Riemann’s uniformly convergent infinite series expansion of ≡(z) involving incomplete gamma functions. We conjecture that when the zeros of ≡N(z) in the first quadrant of the complex plane are listed by increasing real part, their imaginary parts are monotone nondecreasing. We show how this...
Spectral statistics.