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.
Power-free values, large deviations, and integer points on irrational curves
Let be a polynomial of degree without roots of multiplicity or . Erdős conjectured that, if satisfies the necessary local conditions, then is free of th powers for infinitely many primes . This is proved here for all with sufficiently high entropy.The proof serves to demonstrate two innovations: a strong repulsion principle for integer points on curves of positive genus, and a number-theoretical analogue of Sanov’s theorem from the theory of large deviations.
Powerful values of quadratic polynomials.
Poznámka o číslech spřízněných
Pretentiousness in analytic number theory
In this report, prepared specially for the program of the XXVième Journées Arithmétiques, we describe how, in joint work with K. Soundararajan and Antal Balog, we have developed the notion of “pretentiousness” to help us better understand several key questions in analytic number theory.
Prime constellations in triangles with binomial coefficient congruences
The primality of numbers, or of a number constellation, will be determined from residue solutions in the simultaneous congruence equations for binomial coefficients found in Pascal’s triangle. A prime constellation is a set of integers containing all prime numbers. By analyzing these congruences, we can verify the primality of any number. We present different arrangements of binomial coefficient elements for Pascal’s triangle, such as by the row shift method of Mann and Shanks and especially by...
Prime divisors of polynomials at consecutive integers.
Prime divisors of some shifted products.
Prime facto rs of consecutive integers.