"Maass forms"의 두 판 사이의 차이

2013년 3월 28일 (목) 15:43 판

Hyperbolic distribution problems and half-integral weight Maass forms
Automorphic forms correspond to representations that occur in $L_2(G/\Gamma)$. In the case when $G$ is $SL_2$, holomorphic modular forms correspond to (highest weight vectors of) discrete series representations of $G$, while Maass wave forms correspond to (spherical vectors of) continuous series representations of G.

Henryk Iwaniek, Emmanuel Kowalski (2004). Analytic number theory
Lectures on modular functions of one complex variable (Tata Institute of Fundamental Research. Lectures on mathematics and physics. Mathematics, 29)
- Hans Maass, (pdf)

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 ==Kloosterman sum==
+* {{수학노트|url=클루스터만_합}}
-* used to estimate the Fourier coefficients of modular forms
-* definition for prime p
-:<math>S(a,b;p)=\sum_{1\leq x\leq p-1}{\exp(2i\pi (ax+b\bar{x})/p)},\quad\text{where}\quad x\bar{x}\equiv 1\text{ mod } p</math><br>
-* generally defined as
-:<math>K(a,b;m)=\sum_{0\leq x\leq m-1,\ gcd(x,m)=1 } e^{2\pi i (ax+bx^*)/m}</math><br>
-* http://blogs.ethz.ch/kowalski/2010/02/26/the-fourth-moment-of-kloosterman-sums/
-* Kloosterman, H. D. [http://www.springerlink.com/content/cq7681384842j128/?p=5679d1bb49fd45a3987db6d83a1147b6&pi=1 On the representation of numbers in the form ax² + by² + cz² + dt²], Acta Mathematica 49 (1926), pp. 407-464
-==history==
-* http://www.google.com/search?hl=en&tbs=tl:1&q=
@@ 54번째 줄: / 37번째 줄: @@
 * http://en.wikipedia.org/wiki/Kronecker_limit_formula
 * http://en.wikipedia.org/wiki/Real_analytic_Eisenstein_series
-* http://en.wikipedia.org/wiki/Kloosterman_sum
 ==question and answers(Math Overflow)==
 * http://mathoverflow.net/questions/52744/what-is-the-relationship-between-modular-forms-and-maass-forms
-* http://mathoverflow.net/search?q=
 [[분류:개인노트]]