The Haros-Farey sequence at two hundred years. A survey.
The Hawkins sieve and brownian motion
The Hooley-Huxley contour method for problems in number fields III : frobenian functions
In this paper we study finite valued multiplicative functions defined on ideals of a number field and whose values on the prime ideals depend only on the Frobenius class of the primes in some Galois extension. In particular we give asymptotic results when the ideals are restricted to “small regions”. Special cases concern Ramanujan's tau function in small intervals and relative norms in “small regions” of elements from a full module of the Galois extension.
The hyperbola
We include several results providing bounds for an interval on the hyperbola containing lattice points.
The iterated Carmichael λ-function and the number of cycles of the power generator
The joint distribution of additive and complex-valued multiplicative functions
In the paper the necessary and sufficient conditions for the existence of joint limit distribution for real additive and complex-valued multiplicative function are presented.
The joint distribution of -additive functions on polynomials over finite fields
Let be a finite field and a polynomial of positive degree. A function on is called (completely) -additive if , where and . We prove that the values are asymptotically equidistributed on the (finite) image set
The joint distribution of q-additive functions
The jumping champions of the Farey series
The k-functions in multiplicative number theory. I. On complex explicit formulae
The k-functions in multiplicative number theory. II. Uniform distribution of zeta zeros
The k-functions in multiplicative number theory. III. Uniform distribution of zeta zeros; discrepancy
The k-functions in multiplicative number theory. IV. On a method of A. E. Ingham
The k-functions in multiplicative number theory. V. Changes of sign of some arithmetical error terms
The k-tuple jumping champions among consecutive primes
The large sieve in Riemann surfaces
The largest prime factor of X³ + 2
Improving on a theorem of Heath-Brown, we show that if X is sufficiently large then a positive proportion of the values n³ + 2: n ∈ (X,2X] have a prime factor larger than .
The least pair of consecutive character non-residues.
The least prime in an arithmetic progression with prime difference.
The least prime primitive root and the shifted sieve