Related papers: Asymptotics of class numbers
The paper presents a discussion on the asymptotic formula for the number of plane partitions of a large positive integer.
We derive asymptotic formulae for the coefficients of bivariate generating functions with algebraic and logarithmic factors. Logarithms appear when encoding cycles of combinatorial objects, and also implicitly when objects can be broken…
A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…
A certain class of directed metric graphs is considered. Asymptotics for a number of possible endpoints of a random walk at large times is found.
Using estimates on Hooley's $\Delta$-function and a short interval version of the celebrated Dirichlet hyperbola principle, we derive an asymptotic formula for a class of arithmetic functions over short segments. Numerous examples are also…
In this paper we give an asymptotic expansion including error terms for the number of cycles in homology classes for connected graphs. Mainly, we obtain formulae about the coefficients of error terms which depend on the homology classes and…
We derive an analytic class number formula valid for an order in a product of $S$-integers in global fields, or equivalently for reduced finite-type affine schemes of pure dimension $1$ over $\mathbb{Z}$.
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result…
We extend known results on the number of solutions to a linear equation in at least three prime numbers when the primes involved are required to lie in specified Chebotarev classes. We prove asymptotic results similar to previous ones only…
We obtain an asymptotic formula for the number of ways to represent every reduced residue class as a product of a prime and square-free integer. This may be considered as a relaxed version of a conjecture of Erd\"os, Odlyzko, and…
An asymptotic formula with a square root error term is obtained for the number of elements with given trace and norm in a finite semisimple algebra over a finite field. This extends previous results from finite etale algebras (commutative…
We deduce from Arthur's trace formula a formula with only orbital integrals on the geometric side.
It is shown that the class number for negative discriminant $D$ can be expressed in terms of the base $B$ expansions of reduced fractions $\frac{x}{|D|}$, where $B$ is an integer prime to $D$. This result is then formulated to obtain…
An asymptotic formula is given for the number of y-smooth numbers up to x in a Beatty sequence corresponding to an irrational number of finite type.
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
We develop a method for computing all the {\it generalized asymptotes} of a real plane algebraic curve $\cal C$ over $\Bbb C$ implicitly defined by an irreducible polynomial $f(x,y)\in {\Bbb R}[x,y]$. The approach is based on the notion of…
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.
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
This note contains some asymptotic formulas for the sums of various residue classes of Euler's phi-function.