Sets of integers composed of few prime numbers
Sets of integers with pairwise common divisor and a factor from a specified set of primes
Sets of Primes with Intermediate Density.
Sharp elementary estimates for the sequence of primes
Shifted B-numbers as a set of uniqueness for additive and multiplicative functions
Shifted primes without large prime factors
Shifted values of the largest prime factor function and its average value in short intervals
We obtain estimates for the average value of the largest prime factor P(n) in short intervals [x,x+y] and of h(P(n)+1), where h is a complex-valued additive function or multiplicative function satisfying certain conditions. Letting stand for the sum of the digits of n in base q ≥ 2, we show that if α is an irrational number, then the sequence is uniformly distributed modulo 1.
Short interval results for k-free values of irreducible polynomials
Short intervals almost all containing primes
Short sums of restricted Möbius functions
Sieve methods and class-number probelms. II.
Sieve methods and class-number problems. I.
Sieve methods and class-number problems III.
Sieve methods and polynomial sequences
Sieving by Large Prime Factors.
Sieving by prime powers
Sign changes in
Sign changes of error terms related to arithmetical functions
Let . Motivated by a conjecture of Erdös, Lau developed a new method and proved that We consider arithmetical functions whose summation can be expressed as , where is a polynomial, and . We generalize Lau’s method and prove results about the number of sign changes for these error terms.
Small discriminants of complex multiplication fields of elliptic curves over finite fields
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves over a prime finite field of elements, such that the discriminant of the quadratic number field containing the endomorphism ring of over is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I. E. Shparlinski (2007).
Small gaps between zeros of twisted L-functions