Weighted averages of Bernoulli polynomials and the Gamma function over regular integers modulo $n$

Waseem Alass; Sumaia Saad Eddin

Weighted averages of Bernoulli polynomials and the Gamma function over regular integers modulo $n$

Number Theory 2026-08-02 v1

Authors: Waseem Alass , Sumaia Saad Eddin

Abstract

We investigate weighted averages involving Bernoulli polynomials and the Gamma function over regular integers modulo n. Building upon recent identities of Kiuchi and Matsuoka together with our previous transformation formulas for weighted averages over regular integers, we derive explicit asymptotic formulas for a broad class of arithmetic functions. As applications, asymptotic formulas are obtained for the identity, M\"obius, divisor and Jordan totient functions.

Keywords

Bernoulli polynomials Gamma function regular integers weighted averages asymptotic formulas arithmetic functions

Cite

@article{arxiv.2608.01399,
  title  = {Weighted averages of Bernoulli polynomials and the Gamma function over regular integers modulo $n$},
  author = {Waseem Alass and Sumaia Saad Eddin},
  journal= {arXiv preprint arXiv:2608.01399},
  year   = {2026}
}

Comments

17 pages