Finite trigonometric sums arising from Ramanujan’s theta functions

Bruce C. Berndt; Sun Kim; Alexandru Zaharescu

doi:10.1007/s11139-023-00778-2

Finite trigonometric sums arising from Ramanujan’s theta functions

Bruce C. Berndt
, Sun Kim^*
, Alexandru Zaharescu

^*Corresponding author for this work

Department of Mathematics

University of Illinois at Urbana-Champaign
Romanian Academy

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

6 Scopus citations

Abstract

Two classes of finite trigonometric sums, each involving only sines, are evaluated in closed form. The previous and original proofs arise from Ramanujan’s theta functions and modular equations.

Original language	English
Pages (from-to)	673-685
Number of pages	13
Journal	Ramanujan Journal
Volume	63
Issue number	3
DOIs	https://doi.org/10.1007/s11139-023-00778-2
State	Published - 2024.03

Keywords

33B10
Finite trigonometric sums
Primary 11L03
Ramanujan’s modular equations
Theta functions

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1007/s11139-023-00778-2

Cite this

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title = "Finite trigonometric sums arising from Ramanujan{\textquoteright}s theta functions",

abstract = "Two classes of finite trigonometric sums, each involving only sines, are evaluated in closed form. The previous and original proofs arise from Ramanujan{\textquoteright}s theta functions and modular equations.",

keywords = "33B10, Finite trigonometric sums, Primary 11L03, Ramanujan{\textquoteright}s modular equations, Theta functions",

author = "Berndt, \{Bruce C.\} and Sun Kim and Alexandru Zaharescu",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.",

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AU - Berndt, Bruce C.

AU - Kim, Sun

AU - Zaharescu, Alexandru

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2023.

PY - 2024/3

Y1 - 2024/3

N2 - Two classes of finite trigonometric sums, each involving only sines, are evaluated in closed form. The previous and original proofs arise from Ramanujan’s theta functions and modular equations.

AB - Two classes of finite trigonometric sums, each involving only sines, are evaluated in closed form. The previous and original proofs arise from Ramanujan’s theta functions and modular equations.

KW - 33B10

KW - Finite trigonometric sums

KW - Primary 11L03

KW - Ramanujan’s modular equations

KW - Theta functions

UR - https://www.scopus.com/pages/publications/85171130561

U2 - 10.1007/s11139-023-00778-2

DO - 10.1007/s11139-023-00778-2

M3 - Journal article

AN - SCOPUS:85171130561

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VL - 63

SP - 673

EP - 685

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

ER -

Finite trigonometric sums arising from Ramanujan’s theta functions

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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