RESTRICTED CONVOLUTION SUMS OF DIVISOR FUNCTIONS FOR PRIME POWERS

Gye Hwan Jo; Daeyeoul Kim

doi:10.4134/JKMS.j250462

RESTRICTED CONVOLUTION SUMS OF DIVISOR FUNCTIONS FOR PRIME POWERS

Gye Hwan Jo
, Daeyeoul Kim

Department of Mathematics

Jeonbuk National University

Research output: Contribution to journal › Journal article › peer-review

Abstract

We investigate restricted convolution sums of divisor functions formed by coprime summation variables. For the nine classical Ramanujan pairs (k, h), we derive explicit formulas for R_k,h(p^α) at prime powers. As a main application, we compute the exact p-adic valuation of R_k,h(p^α) and demonstrate its linear growth with α.

Original language	English
Pages (from-to)	849-877
Number of pages	29
Journal	Journal of the Korean Mathematical Society
Volume	63
Issue number	4
DOIs	https://doi.org/10.4134/JKMS.j250462
State	Published - 2026.07

Keywords

Dirichlet inversion
divisor functions
p-adic valuation
Ramanujan identities
Restricted convolution sum

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10.4134/JKMS.j250462

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title = "RESTRICTED CONVOLUTION SUMS OF DIVISOR FUNCTIONS FOR PRIME POWERS",

abstract = "We investigate restricted convolution sums of divisor functions formed by coprime summation variables. For the nine classical Ramanujan pairs (k, h), we derive explicit formulas for Rk,h(pα) at prime powers. As a main application, we compute the exact p-adic valuation of Rk,h(pα) and demonstrate its linear growth with α.",

keywords = "Dirichlet inversion, divisor functions, p-adic valuation, Ramanujan identities, Restricted convolution sum",

author = "Jo, \{Gye Hwan\} and Daeyeoul Kim",

note = "Publisher Copyright: {\textcopyright} 2026 Korean Mathematical Society.",

year = "2026",

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AU - Kim, Daeyeoul

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N2 - We investigate restricted convolution sums of divisor functions formed by coprime summation variables. For the nine classical Ramanujan pairs (k, h), we derive explicit formulas for Rk,h(pα) at prime powers. As a main application, we compute the exact p-adic valuation of Rk,h(pα) and demonstrate its linear growth with α.

AB - We investigate restricted convolution sums of divisor functions formed by coprime summation variables. For the nine classical Ramanujan pairs (k, h), we derive explicit formulas for Rk,h(pα) at prime powers. As a main application, we compute the exact p-adic valuation of Rk,h(pα) and demonstrate its linear growth with α.

KW - Dirichlet inversion

KW - divisor functions

KW - p-adic valuation

KW - Ramanujan identities

KW - Restricted convolution sum

UR - https://www.scopus.com/pages/publications/105043798078

U2 - 10.4134/JKMS.j250462

DO - 10.4134/JKMS.j250462

M3 - Journal article

AN - SCOPUS:105043798078

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VL - 63

SP - 849

EP - 877

JO - Journal of the Korean Mathematical Society

JF - Journal of the Korean Mathematical Society

IS - 4

ER -

RESTRICTED CONVOLUTION SUMS OF DIVISOR FUNCTIONS FOR PRIME POWERS

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Keywords

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