Asymptotic expansions of finite theta series
Asymptotic expansions of the mean values of Dirichlet L-functions III.
Asymptotic expansions of the mean values of Dirichlet L-functions.
Asymptotic form for generalized factorial
Asymptotic Formula for Distinct Partitions of Lattice Points with Congruence Restrictions.
Asymptotic formula for sum-free sets in abelian groups
Asymptotic formulae.
Asymptotic formulae concerning arithmetical functions defined by cross-convolutions. VI: --free integers.
Asymptotic formulae for partition ranks
Using an extension of Wright's version of the circle method, we obtain asymptotic formulae for partition ranks similar to formulae for partition cranks which where conjectured by F. Dyson and recently proved by the first author and K. Bringmann.
Asymptotic Formulae for the Coefficients of a Class of Modular Forms.
Asymptotic formulas and generalized Dedekind sums.
Asymptotic formulas for the coefficients of certain automorphic functions
We derive asymptotic formulas for the coefficients of certain classes of weakly holomorphic Jacobi forms and weakly holomorphic modular forms (not necessarily of integral weight) without using the circle method. Then two applications of these formulas are given. Namely, we estimate the growth of the Fourier coefficients of two important weak Jacobi forms of index 1 and non-positive weights and obtain an asymptotic formula for the Fourier coefficients of the modular functions for all integers k,l...
Asymptotic growth of Markoff-Hurwitz numbers
Asymptotic mean square of the product of the Riemann zeta-function and a Dirichlet polynomial.
Asymptotic nature of higher Mahler measure
We consider Akatsuka’s zeta Mahler measure as a generating function of the higher Mahler measure of a polynomial where is the integral of over the complex unit circle. Restricting ourselves to P(x) = x - r with |r| = 1 we show some new asymptotic results regarding , in particular as k → ∞.
Asymptotic order of the square-free part of .
Asymptotic properties of Dedekind zeta functions in families of number fields
The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer–Siegel theorem. As an application we obtain a limit formula for Euler–Kronecker constants in families of number fields.
Asymptotic representations for Fibonacci reciprocal sums and Euler’s formulas for zeta values
We present asymptotic representations for certain reciprocal sums of Fibonacci numbers and of Lucas numbers as a parameter tends to a critical value. As limiting cases of our results, we obtain Euler’s formulas for values of zeta functions.
Asymptotic Results for a Class of Arithmetical Functions.
Asymptotic sieve for primes.