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Tag Archives: Hensel’s Lemma

Large Prime Factors of a Quadratic Polynomial

March 30, 2018by Alexander Walker Leave a comment

One of Landau’s four problems from 1912 concerns the infinitude of primes in the values of a certain quadratic polynomial.

In this post, we show that the largest prime factors of the values of this polynomial are “relatively large” infinitely often.

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analytic number theory, number theory, sieve theory

Counting Real Quadratic Fields Without Unique Factorization

February 5, 2017by Alexander Walker Leave a comment

The full list of imaginary quadratic fields with unique factorization has been determined, but it remains unknown whether or not infinitely many real quadratic fields are UFDs. Here, we develop a simple criterion for disproving unique factorization based on continued fractions and use this to give upper bounds.

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number theory

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You have stumbled upon the personal blog of Alex Walker. I am a number theorist and a Heilbronn fellow at UCL.

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