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Mathoverflow.net news digest

  • 0 days

    Largest prime divisors of some sequences

    Let $P(n)$ be the largest prime factor of $n$. One can check that $11$ is the smallest prime that does not appear as the largest prime factor of a Mersenne number, $P(2^k-1)$. But note that $11=2^2×3-1$. What happens If we ask for the possible values...

  • 0 days

    From geometric to function field Langlands

    I came across the following paper of Gaitsgory a couple of days ago
    https://arxiv.org/pdf/1606.09608.
    I was wondering whether there exists a proof of the Langlands program over function field using the above? The techniques used by Vincent Lafforgue are disjoint from this as far as I know. Does it shades any light on the Langlands conjecture over global...

  • 6 days

    Is the condition about composition needed to stay with the elementary functions?

    This question was first asked here, and Qiaochu Yuan gave a partial answer, but there is a gap in his answer, and thus requires more work.
    We use the definition of elementary functions given in Spivak's calculus (with some changes so this is not exactly the same). An elementary function isone which can be obtained by a finite number of operations of addition, multiplication, division, and...

  • 1 month

    Teaching physics to mathematicians

    EDIT: I believe that interactions between physics and mathematics are widely appreciated today. However, my impression is that many mathematicians still find it difficult to understand the physicists’ style of thinking, particularly the relative lack...

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