On the upper bound for π₂(x)
On twin almost primes
On two conjectures of Kátai
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.
Oscillatory properties of , I
in short intervals
For any sufficiently large real number , the interval contains at least one integer having at most two prime factors .
p+a without large prime factors.
Perfect powers in products of integers from a block of consecutive integers
Potenzfreie Werte von Polynomen in algebraischen Zahlkörpern.
Prime divisors of polynomials at consecutive integers.
Prime facto rs of consecutive integers.
Prime numbers along Rudin–Shapiro sequences
For a large class of digital functions , we estimate the sums (and , where denotes the von Mangoldt function (and the Möbius function). We deduce from these estimates a Prime Number Theorem (and a Möbius randomness principle) for sequences of integers with digit properties including the Rudin-Shapiro sequence and some of its generalizations.
Prime numbers in short intervals
Prime numbers of the form p = m²+n²+1 in short intervals
Prime percolation.
Primes and power-primes
Primes and zeros in short intervals.
Primes in almost all short intervals
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 in intervals