Work

Periodic minimum in the count of binomial coefficients not divisible by a prime

Year: 2025

Type: article

Abstract: The summatory function of the number of binomial coefficients not divisible by a prime is known to exhibit regular periodic oscillations, yet identifying the less regularly behaved minimum of the underlying periodic functions has been open for almost all cases. We propose an approach to identify such minimum in some generality, solving particularly a previous conjecture of B. Wilson [Acta Arith. 83 (1998), 105–116].

Source: Mathematics of Computation

DOI: 10.1090/mcom/4108

Authors: Hsien-Kuei Hwang, Svante Janson, Tsung-Hsi Tsai

Institutions: Institute of Statistical Science, Academia Sinica, Academia Sinica, Uppsala University

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Knut och Alice Wallenbergs Stiftelse, Vetenskapsrådet, Ministry of Science and Technology, Taiwan

Awards: Sensitivity Analysis of Combinatorial Distributions, G1956604466, G4253916272