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1d
comment When does the radius of convergence of the product of two $p$-adic power series increase?
In general if $F(x)$ and $F(x)^{-1}$ have a common radius of convergence $R$, and $G(x)$ and $G(x)^{-1}$ have a common radius of convergence $S$ then the product $FG$ has radius of convergence $\min(R,S)$ if $R \not= S$. If $R=S$ then there is no simple rule for the radius of $FG$. Typically the radius for $FG$ will remain $R$, but of course there are examples where it grows, like $\exp(x)$ and $\exp(x^p/p)$, or more simply $\exp(x)$ and $\exp(-x)$.
2d
revised When does the radius of convergence of the product of two $p$-adic power series increase?
deleted 341 characters in body
2d
revised When does the radius of convergence of the product of two $p$-adic power series increase?
added 690 characters in body
2d
answered When does the radius of convergence of the product of two $p$-adic power series increase?
Feb
5
comment mod 5 partition identity proof
разбиение на n частей = partition into n parts.
Feb
5
revised mod 5 partition identity proof
edited body
Feb
5
comment Roadmap for the ideas expressed in Grothendieck's Esquisse d'un Programme
Look here: cambridge.org/us/academic/subjects/mathematics/number-theory/…
Feb
3
revised Quaternion algebra in characteristic $p$
edited title
Feb
3
comment Quaternion algebra in characteristic $p$
@abx, not when $p=2$...
Jan
28
comment What is the mathematical significance of the IHES logo?
Great question! I've wondered this myself several times over the years.
Jan
15
awarded  Yearling
Jan
12
revised Why are they called L-functions?
deleted 1 character in body
Jan
12
revised Why are they called L-functions?
deleted 1 character in body
Jan
12
revised Why are they called L-functions?
added 466 characters in body
Jan
8
comment How to cite authors from any country correctly?
Concerning Chebyshev, see math.tamu.edu/~boas/courses/math696/spelling-lesson.html.
Jan
5
comment Showing the positivity of $p$-adic density of zeroes of a polynomial
Did you know that Hensel's lemma can be formulated in a way that does not require nonsingular roots mod p? Instead of requiring an $a \in \mathbf Z_p$ such that $f(a) \equiv 0 \bmod p$ and $f'(a) \not\equiv 0 \bmod p$, it's enough to have an $a$ such that $|f(a)|_p < |f'(a)|_p^2$. And this inequality is satisfied by all $a$ that are close to a nonsingular root in $\mathbf Z_p$. See Theorem 7.1 of math.uconn.edu/~kconrad/blurbs/gradnumthy/hensel.pdf. Your multivariable situation can be reduced to the one-variable situation by fixing all but one coordinate of a nonsingular solution.
Jan
3
comment Hecke character and CM elliptic curve
Do you know how to express the $L$-function of a non-normalized Hecke character $\chi$ in terms of the $L$-function of its normalized form $\chi'$?
Jan
3
comment Does differentiation widen, or narrow, the class of functions?
The impression students may get from a calculus class is the complete opposite of what analysts know well: differentiation tends to make functions worse while integration makes them better.
Jan
1
comment Rings that inject in all p-adic integers
That $F$ is $\widehat{\mathbf Z}$ can be found in some notes of Lenstra, who either defines $\widehat{\mathbf Z}$ that way or makes it an exercise to show this: euro-math-soc.eu/system/files/news/…, math.leidenuniv.nl/~hwl/papers/fibo.pdf, and websites.math.leidenuniv.nl/algebra/Lenstra-Profinite.pdf.
Dec
26
awarded  Nice Answer