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4 questions
1
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1
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260
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Conceptual explanation for extra/missing $p$ solutions to $x^2+y^2=a \pmod p$ at $a=0$
Throughout, $p$ will denote a prime integer, and $k$ an arbitrary integer.
I have worked through V. Lebesgue's proof of quadratic reciprocity outlined by Keith Conrad in this MO thread, and I feel ...
- 833
21
votes
2
answers
2k
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Context for "Coronidis Loco" from Weil's Basic Number Theory
In Samuel James Patterson's article titled Gauss Sums in The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae, Patterson says
"Hecke [proved] a beautiful theorem on the different ...
- 7,062
1
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1
answer
215
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Computation of Hilbert symbol of order 4
We have explicit expressions for the quadratic Hilbert symbol over $\mathbb Q$, for example $\left(\dfrac{x,y}2\right)_2=(-1)^{\frac{x-1}2\frac{y-1}2} (x,y\ne2)$. Are similar expressions known for the ...
- 13
3
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0
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165
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Averages of $L(s,\chi)$
Let $(\frac{m}{n})$ denote the usual quadratic Jacobi symbol.
What is the
abscissa of convergence
of the double Dirichlet series ?
$$
\sum_{\substack{m,n \in \mathbb{N} \\ \gcd(m,n)=1 \\m,n\equiv 1 \...
- 3,062