Add to ORKGLet R(n,x) be the number of modular inverses modulo n that are less than x. It is well-known (e.g. Heath-Brown) that R(p,p^{3/4+\epsilon})\gg p^{1/2+\epsilon} for primes p. An open problem is to improve the exponent 3/4. In the talk, I will introduce how to study the average version of the problem in terms of the dynamics of continued fractions. This is research in progress
The evenness and the values modulo $4$ of the lengths of the periods of the continued fraction expan...
International audienceWe study the limiting distributions of Birkhoff sums of a large class of cost ...
We consider a generalisation of the classical Lehmer problem about the distribution of modular inver...
Counting the number of modular inverses with respect to a fixed modulus in a given interval is quite...
Let p> 2 be a prime number. For each integer 0 < n < p, de¯ne n by the congruence nn ´ 1 (m...
International audienceWe study algorithms for the fast computation of modular inverses. Newton-Raphs...
International audienceThe evenness and the values modulo 4 of the lengths of the periods of the cont...
Modular partition vector is a generalization of the length of continued fraction to a nontrivial con...
As a sequel to some recent works of Berndt and Baruah and Saikia we evaluate G(e(-Pirootn)) for cert...
Abstract. Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss{Kuzm...
We show that the exponent of distribution of the ternary divisor function $d_{3}$ in arithmetic prog...
AbstractWe investigate the distribution of the numbers x∈[1,p] for which a1x+b1,…,asx+bs(modp) all l...
Let p be a prime ≡ 1 (mod 4) such that the norm of the fundamental unit of Q(√2p) is −1. A necessary...
For some natural families of elliptic curves we show that "on average" the exponent of the point gro...
In a recent work, Shallit and Vasiga have obtained several results about tails and cycles in orbits ...
The evenness and the values modulo $4$ of the lengths of the periods of the continued fraction expan...
International audienceWe study the limiting distributions of Birkhoff sums of a large class of cost ...
We consider a generalisation of the classical Lehmer problem about the distribution of modular inver...
Counting the number of modular inverses with respect to a fixed modulus in a given interval is quite...
Let p> 2 be a prime number. For each integer 0 < n < p, de¯ne n by the congruence nn ´ 1 (m...
International audienceWe study algorithms for the fast computation of modular inverses. Newton-Raphs...
International audienceThe evenness and the values modulo 4 of the lengths of the periods of the cont...
Modular partition vector is a generalization of the length of continued fraction to a nontrivial con...
As a sequel to some recent works of Berndt and Baruah and Saikia we evaluate G(e(-Pirootn)) for cert...
Abstract. Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss{Kuzm...
We show that the exponent of distribution of the ternary divisor function $d_{3}$ in arithmetic prog...
AbstractWe investigate the distribution of the numbers x∈[1,p] for which a1x+b1,…,asx+bs(modp) all l...
Let p be a prime ≡ 1 (mod 4) such that the norm of the fundamental unit of Q(√2p) is −1. A necessary...
For some natural families of elliptic curves we show that "on average" the exponent of the point gro...
In a recent work, Shallit and Vasiga have obtained several results about tails and cycles in orbits ...
The evenness and the values modulo $4$ of the lengths of the periods of the continued fraction expan...
International audienceWe study the limiting distributions of Birkhoff sums of a large class of cost ...
We consider a generalisation of the classical Lehmer problem about the distribution of modular inver...