Functions and mappings | Algebraic geometry

Motivic zeta function

In algebraic geometry, the motivic zeta function of a smooth algebraic variety is the formal power series Here is the -th symmetric power of , i.e., the quotient of by the action of the symmetric group , and is the class of in the ring of motives (see below). If the ground field is finite, and one applies the counting measure to , one obtains the local zeta function of . If the ground field is the complex numbers, and one applies Euler characteristic with compact supports to , one obtains . (Wikipedia).

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Some identities involving the Riemann-Zeta function.

After introducing the Riemann-Zeta function we derive a generating function for its values at positive even integers. This generating function is used to prove two sum identities. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Riemann Zeta Function

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By applying some combinatorial tricks to an identity from https://youtu.be/2W2Ghi9idxM we are able to derive two identities involving the Riemann-Zeta function. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist The Riemann Zeta Function

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From playlist Transcendental Functions

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From playlist Transcendental Functions

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From playlist Programming

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From playlist The Sato-Tate conjecture for abelian varieties

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From playlist ELLIPTIC CURVES AND THE SPECIAL VALUES OF L-FUNCTIONS (2022)

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