# On the periodicity of trigonometric functions generalized to quotient rings of R[x]

Open Mathematics (2006)

- Volume: 4, Issue: 3, page 395-412
- ISSN: 2391-5455

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topClaude Gauthier. "On the periodicity of trigonometric functions generalized to quotient rings of R[x]." Open Mathematics 4.3 (2006): 395-412. <http://eudml.org/doc/269604>.

@article{ClaudeGauthier2006,

abstract = {We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.},

author = {Claude Gauthier},

journal = {Open Mathematics},

keywords = {30G35; 11M41},

language = {eng},

number = {3},

pages = {395-412},

title = {On the periodicity of trigonometric functions generalized to quotient rings of R[x]},

url = {http://eudml.org/doc/269604},

volume = {4},

year = {2006},

}

TY - JOUR

AU - Claude Gauthier

TI - On the periodicity of trigonometric functions generalized to quotient rings of R[x]

JO - Open Mathematics

PY - 2006

VL - 4

IS - 3

SP - 395

EP - 412

AB - We apply a method of Euler to algebraic extensions of sets of numbers with compound additive inverse which can be seen as quotient rings of R[x]. This allows us to evaluate a generalization of Riemann’s zeta function in terms of the period of a function which generalizes the function sin z. It follows that the functions generalizing the trigonometric functions on these sets of numbers are not periodic.

LA - eng

KW - 30G35; 11M41

UR - http://eudml.org/doc/269604

ER -

## References

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