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The goal is to study new Lambda functions at roots of unity and derive their numerical values and properties.

March 17, 2026Open Access

New Lambda functions at the roots of unity with special values and infinite series.

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Part 3 investigates Lambda functions at roots of unity, revealing special values and patterns in calculations.

The goal is to study new Lambda functions at roots of unity and derive their numerical values and properties.
Calculated Lambda functions at ω = 1, -1, i, -i, e^{2πi/3}, e^{4πi/3} using high-precision summation.
Examined conjugation symmetry in the functions across different roots of unity.
Derived exact closed forms for specific values of k and roots of unity based on advanced mathematical functions.
Numerical values for Λ₂(i) and Λ₃(i) match direct summation with high precision (within 10⁻⁵ and 4×10⁻⁸, respectively).
Symmetry is consistently observed in the Lambda functions for all tested values of ω.
Closed forms for the functions are established, giving insights into their behavior at roots of unity.

Muzzamal Hussain (2026) studied this question.

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March 17, 2026Open Access

View Full Paper

Ask AI

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Authors

Part 3 investigates Lambda functions at roots of unity, revealing special values and patterns in calculations.

The goal is to study new Lambda functions at roots of unity and derive their numerical values and properties.
Calculated Lambda functions at ω = 1, -1, i, -i, e^{2πi/3}, e^{4πi/3} using high-precision summation.
Examined conjugation symmetry in the functions across different roots of unity.
Derived exact closed forms for specific values of k and roots of unity based on advanced mathematical functions.
Numerical values for Λ₂(i) and Λ₃(i) match direct summation with high precision (within 10⁻⁵ and 4×10⁻⁸, respectively).
Symmetry is consistently observed in the Lambda functions for all tested values of ω.
Closed forms for the functions are established, giving insights into their behavior at roots of unity.

Muzzamal Hussain (2026) studied this question.

View Full Paper

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