相关论文: Class numbers of orders in cubic fields

Let $x$ be a positive integer. We give an asymptotic formula for the number of primes in the set $\{\fl{x/n}, 1 \le n \le x\}$ and give some related results.

In this paper, we consider a Class of Hessian quotient equations in Euclidean space. Under some sufficient condition, we obtain an existence result by the standard degree theory based on the a prior estimates for the solutions to the…

We present an explicit formula computing morphism spaces in the stable category of a Frobenius algebra.

In the present paper we prove that for any fixed $1<c<7/6$ there exist infinitely many consecutive square-free numbers of the form $[n^c], [n^c]+1$ and we also establish an asymptotic formula in given interval.

We remove logarithmic factors in error term estimates in asymptotic formulas for the number of solutions of a class of additive congruences modulo a prime number.

One can define class invariants for a quartic primitive CM field K as special values of certain Siegel (or Hilbert) modular functions at CM points corresponding to K. We provide explicit bounds on the primes appearing in the denominators of…

We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with Tamari intervals. We show that in each…

In this note we present techniques to compute inhomogeneous minima of norm forms; as an application, we determine all norm-Euclidean complex bicyclic quartic number fields.

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2,2,2) whose Hilbert 2-class fields are finite.

We exhibit a procedure to asymptotically enumerate monotone grid classes of permutations. This is then applied to compute the asymptotic number of permutations in any connected one-corner class. Our strategy consists of enumerating the…

For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied…

We prove that a finite type curve is an $\xi$-asymptotic line (without parabolic points) of a suitable plane field. It is also given an explicit example of a hyperbolic closed finite type $\xi$-asymptotic line. These results obtained here…

We give an asymptotic formula for the number of monic Eisenstein polynomials of odd prime degree satisfying an additional condition that arises in the study of the genus number of an algebraic number field.

We establish asymptotic formulas for the number of integral points of bounded height on toric varieties.

Many asymptotic formulas exist for unrestricted integer partitions as well as for distinct partitions of integers into a finite number of parts. Szekeres and Canfield have derived an asymptotic formula for the number of partitions that is…

In this paper we determine the group of rational automorphisms of binary cubic and quartic forms with integer coefficients and non-zero discriminant in terms of certain quadratic covariants of cubic and quartic forms. This allows one to…

In this paper, we are interested in the interplay between integral ternary quadratic forms and class numbers. This is partially motivated by a question of Petersson.

We construct a random model to study the distribution of class numbers in special families of real quadratic fields $\mathbb Q(\sqrt d)$ arising from continued fractions. These families are obtained by considering periodic continued…

In the paper, we study the asymptotic distribution of real algebraic integers of fixed degree as their naive height tends to infinity. Let $I \subset \mathbb{R}$ be an arbitrary bounded interval, and $Q$ be a sufficiently large number. We…

We prove a higher order asymptotic formula for traces of finite block Toeplitz matrices with symbols belonging to H\"older-Zygmund spaces. The remainder in this formula goes to zero very rapidly for very smooth symbols. This formula refine…