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The Distribution of Zeros in ζ(s) and its Arithmetic Consequences
To kick things off: what is ζ(s)? It’s a function from the complex plane to itself, defined as follows: ζ(s) = 1/1^s + 1/2^s…
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Prime Number Theorem and its Analogue for Irreducible Polynomials
Specifically, we’ll be discussing their analogue for irreducible polynomials in algebraic number theory. But first, let’s take a quick refresher on what exactly these…
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Approximating Pi using Liouville’s Function
In fact, my degree is in computer science and I have no formal training in math beyond high school algebra. However, as someone who…
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The Logarithmic Integral Function
The logarithmic integral has many practical applications, including calculating the number of digits required to represent certain numbers or estimating the size of sets…
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Explicit Upper Bound for Difference Between π(x) and li(x)
What are these mysterious beasts? Well, π(x) is a function that tells us how many prime numbers there are less than or equal to…
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The Prime Number Theorem and Its Connection to Li Function
Instead, let me break it down for you in a way that even my grandma could understand! Well, if you’re not already familiar with…
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Newman’s Factor in Complex Analysis
Now, before you start rolling your eyes and muttering “math is boring,” let me tell you something: math can be fun! And this particular…
