12 citations · 65 across the 28 of their papers we have counts for
34 papers · 1 filter
Some applications of the quasi-Riemann hypothesis to class groups and small generators of number fields
Christopher Frei, Efthymios Sofos, Martin Widmer
We prove an effective version of the Chebotarev density theorem, conditional on the quasi-Riemann hypothesis for the Dedekind zeta function. Drawing on recent breakthroughs of Open…
Serre's problem on statistics of Brauer symbols
Efthymios Sofos
We solve Serre's problem on the specialisation of Brauer group elements in all cases where the number of variables is sufficiently large.
Counting square-free values of random polynomials
Efthymios Sofos
We prove that the average error term when counting square-free values of polynomials is the quartic root of the main term.
On the application of large deviation estimates to local solubility in families of varieties
Sun Woo Park, Efthymios Sofos
We apply the Gärtner--Ellis theorem on large deviations to prove a weak version of the Loughran--Smeets conjecture for general fibrations.
Local solubility in generalised Châtelet varieties
Kevin Destagnol, Julian Lyczak, Efthymios Sofos
We obtain asymptotic formulas for averages of general multivariate arithmetic functions evaluated at polynomial arguments using recent work of Rydin Myerson and Rome-Yamagishi. We…
Averages of arithmetic functions over polynomials in many variables
Kevin Destagnol, Efthymios Sofos
We estimate the average of any arithmetic function over the values of any smooth polynomial in many variables provided only that has a distribution in arithmetic progressio…
Diophantine stability and second order terms
Carlo Pagano, Efthymios Sofos
We establish a Galois-theoretic trichotomy governing Diophantine stability for genus curves. We use it to prove that the curve associated to the Hilbert symbol is Diophantine s…
Elliptic fibrations and
Peter Koymans, Carlo Pagano, Efthymios Sofos
We determine the order of magnitude for all exponential moments of the rank in a broad class of elliptic fibrations and for the -torsion in the class group of quadrati…
Averages of multiplicative functions along equidistributed sequences
Stephanie Chan, Peter Koymans, Carlo Pagano +1
For a general family of non-negative functions matching upper and lower bounds are established for their average over the values of any equidistributed sequence.
-torsion and integral points on quartic threefolds
Stephanie Chan, Peter Koymans, Carlo Pagano +1
We prove matching upper and lower bounds for the average of the 6-torsion of class groups of quadratic fields. Furthermore, we count the number of integer solutions on an affine qu…
Statistics of small prime quadratic non-residues
Efthymios Sofos
We prove that the average of the -th smallest prime quadratic non-residue modulo a prime approximates the -th smallest prime.
Generic diagonal conic bundles revisited
Alexei N. Skorobogatov, Efthymios Sofos
We prove a stronger form of our previous result that Schinzel's Hypothesis holds for of -tuples of integer polynomials satisfying the usual necessary conditions, where t…
Bateman-Horn, polynomial Chowla and the Hasse principle with probability 1
Tim Browning, Efthymios Sofos, Joni Teräväinen
With probability 1, we assess the average behaviour of various arithmetic functions at the values of degree d polynomials f that are ordered by height. This allows us to establish…
The leading constant for rational points in families
Daniel Loughran, Nick Rome, Efthymios Sofos
We prove asymptotics for Serre's problem on the number of diagonal planar conics with a rational point and use this to put forward a new conjecture on counting the number of variet…
Gaps between prime divisors and analogues in Diophantine geometry
E. Sofos
Erdős considered the second moment of the gap-counting function of prime divisors in 1946 and proved an upper bound that is not of the right order of magnitude. We prove asymptotic…
Schinzel Hypothesis on average and rational points
Alexei N. Skorobogatov, Efthymios Sofos
We resolve Schinzel's Hypothesis (H) for of polynomials of arbitrary degree. We deduce that a positive proportion of diagonal conic bundles over with any given…
Multivariate normal distribution for integral points on varieties
Daniel El-Baz, Daniel Loughran, Efthymios Sofos
Given a variety over , we study the distribution of the number of primes dividing the coordinates as we vary an integral point. Under suitable assumptions, we show that…
Cyclotomic polynomials with prescribed height and prime number theory
Alexandre Kosyak, Pieter Moree, Efthymios Sofos +1
Given any positive integer let denote the height of the cyclotomic polynomial, that is its maximum coefficient in absolute value. It is well known that…
Asymptotics of the -free diffraction measure via discretisation
Nick Rome, Efthymios Sofos
We determine the diffraction intensity of the -free integers near the origin.
The size of the primes obstructing the existence of rational points
Efthymios Sofos
The sequence of the primes for which a variety over has no -adic point plays a fundamental role in arithmetic geometry. This sequence is deterministic, however,…
The density of fibres with a rational point for a fibration over hypersurfaces of low degree
Efthymios Sofos, Erik Visse
We prove asymptotics for the proportion of fibres with a rational point in a conic bundle fibration. The basis of the fibration is a general hypersurface of low degree.
Rational points and prime values of polynomials in moderately many variables
Kevin Destagnol, Efthymios Sofos
We derive the Hasse principle and weak approximation for pencils of certain varieties in the spirit of work by Colliot-Thélène,Sansuc and Harpaz-Skorobogatov-Wittenberg. Our variet…
An Erdős-Kac law for local solubility in families of varieties
Daniel Loughran, Efthymios Sofos
We study probability distributions arising from local obstructions to the existence of -adic points in families of varieties. In certain cases we show that an Erdős-Kac type law…
4-ranks and the general model for statistics of ray class groups of imaginary quadratic number fields
Carlo Pagano, Efthymios Sofos
We extend the Cohen-Lenstra heuristics to the setting of ray class groups of imaginary quadratic number fields, viewed as exact sequences of Galois modules. By asymptotically estim…