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.
Pairs of square-free values of the type ,
We show that there exist infinitely many consecutive square-free numbers of the form , . We also establish an asymptotic formula for the number of such square-free pairs when does not exceed given sufficiently large positive number.
Perfect powers in products of integers from a block of consecutive integers
Periods of sets of lengths: a quantitative result and an associated inverse problem
The investigation of quantitative aspects of non-unique factorizations in the ring of integers of an algebraic number field gives rise to combinatorial problems in the class group of this number field. In this paper we investigate the combinatorial problems related to the function 𝓟(H,𝓓,M)(x), counting elements whose sets of lengths have period 𝓓, for extreme choices of 𝓓. If the class group meets certain conditions, we obtain the value of an exponent in the asymptotic formula of this function...
Permanence de relations de récurrence dans certains développements asymptotiques. (Permanence of recurrence relations in certain asymptotic expansions).
Permutation functions and (n,m)-commutativity of semigroups .
Piatetski-Shapiro sequences
Plus grand facteur premier d'entiers en progression arithmétique
p-Nilpotence, classifying space indecomposability, and other properties of almost all finite groups.
Pointwise ergodic theorems for arithmetic sets
Poisson distribution for a sum of additive functions on shifted primes
Polylogarithms and arithmetic function spaces
Polynômes de ayant un diviseur de degré donné
Polynomial values with small prime divisors
Polynomials taking prime values. (Polynômes prenant des valeurs premières.)
Positive integers such that .
Positive integers such that .
Potenzfreie Werte von Polynomen in algebraischen Zahlkörpern.
Power Series with Multiplicative Coefficients.