Eisenstein series and their applications to some arithmetic identities and congruences

Daeyeoul Kim; Aeran Kim; Ayyadurai Sankaranarayanan

doi:10.1186/1687-1847-2013-84

Eisenstein series and their applications to some arithmetic identities and congruences

Daeyeoul Kim^*
, Aeran Kim
, Ayyadurai Sankaranarayanan

^*Corresponding author for this work

Department of Mathematics

National Institute for Mathematical Sciences
Jeonbuk National University
Tata Institute of Fundamental Research

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

Abstract

Utilizing the theory of elliptic curves over ℂ to the normalized lattice Aτ, its connection to the Weierstrass p-functions and to the Eisenstein series E₄(τ) and E₆(τ), we establish some arithmetic identities involving certain arithmetic functions and convolution sums of restricted divisor functions. We also prove some congruence relations involving certain divisor functions and restricted divisor functions.

Original language	English
Article number	84
Journal	Advances in Difference Equations
Volume	2013
DOIs	https://doi.org/10.1186/1687-1847-2013-84
State	Published - 2013.04

Keywords

Congruence relations
Convolution sums
Divisor functions
Eisenstein series
Q-products
Q-series
Restricted divisor functions

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1186/1687-1847-2013-84

Cite this

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title = "Eisenstein series and their applications to some arithmetic identities and congruences",

abstract = "Utilizing the theory of elliptic curves over ℂ to the normalized lattice Aτ, its connection to the Weierstrass p-functions and to the Eisenstein series E4(τ) and E6(τ), we establish some arithmetic identities involving certain arithmetic functions and convolution sums of restricted divisor functions. We also prove some congruence relations involving certain divisor functions and restricted divisor functions.",

keywords = "Congruence relations, Convolution sums, Divisor functions, Eisenstein series, Q-products, Q-series, Restricted divisor functions",

author = "Daeyeoul Kim and Aeran Kim and Ayyadurai Sankaranarayanan",

year = "2013",

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doi = "10.1186/1687-1847-2013-84",

language = "English",

volume = "2013",

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T1 - Eisenstein series and their applications to some arithmetic identities and congruences

AU - Kim, Daeyeoul

AU - Kim, Aeran

AU - Sankaranarayanan, Ayyadurai

PY - 2013/4

Y1 - 2013/4

N2 - Utilizing the theory of elliptic curves over ℂ to the normalized lattice Aτ, its connection to the Weierstrass p-functions and to the Eisenstein series E4(τ) and E6(τ), we establish some arithmetic identities involving certain arithmetic functions and convolution sums of restricted divisor functions. We also prove some congruence relations involving certain divisor functions and restricted divisor functions.

AB - Utilizing the theory of elliptic curves over ℂ to the normalized lattice Aτ, its connection to the Weierstrass p-functions and to the Eisenstein series E4(τ) and E6(τ), we establish some arithmetic identities involving certain arithmetic functions and convolution sums of restricted divisor functions. We also prove some congruence relations involving certain divisor functions and restricted divisor functions.

KW - Congruence relations

KW - Convolution sums

KW - Divisor functions

KW - Eisenstein series

KW - Q-products

KW - Q-series

KW - Restricted divisor functions

UR - https://www.scopus.com/pages/publications/84893909383

U2 - 10.1186/1687-1847-2013-84

DO - 10.1186/1687-1847-2013-84

M3 - Journal article

AN - SCOPUS:84893909383

SN - 1687-1839

VL - 2013

JO - Advances in Difference Equations

JF - Advances in Difference Equations

M1 - 84

ER -

Eisenstein series and their applications to some arithmetic identities and congruences

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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