Hecke equidistribution For a prime $p\equiv 1\pmod{4}$, we can write $p=a^2+b^2=N(a+bi)$. Therefore
$$
a+bi=p^{1/2}e^{i\varphi}
$$
where $\varphi\in [0,2\pi]$. I know that Hecke proved that $\varphi$ is equidistributed. I am looking for a reference for this nice result. I would be thankful if one can give me a reference. 
 A: One reference is Theorem 6 of Chapter XV
(Density of Primes and Tauberian Theorem) in

S. Lang: Algebraic Number Theory (Addison-Wesley, 1970).

This is probably more general than Hecke's result, but
the case of "equidistribution of ideals and primes in sectors"
of the Gaussian numbers is singled out as Example 2 on page 318.
[No, I didn't know this off the top of my head;
my student David Jao needed this result in the case of 
a real quadratic field for his thesis in 2003, and I looked
in the bibliography to find that he used the Lang reference $-$
or more accurately its second edition (1994) by Springer.]
A: A very down-to-earth treatment of this result of Hecke is in Chapter 5 of the nice book Geometric and Analytic Number Theory, by Hlawka, Schoißengeier, and Taschner. By down-to-earth, I mean that they deal directly with this specific case of Hecke's result, and that they prove it using very little -- the method is a modification of the Korevaar--Newman--Zagier approach to the prime number theorem, and so doesn't need any quantitative zero-free region (just a statement that there are no zeros of the appropriate objects on the line $\Re(s)=1$).
A: If you need the original reference, this is proved in Hecke's articles (here and here) where he introduces the famous $L$-functions associated to Grössencharakteren.
E. Hecke, Eine neue Art von Zetafunktionen und ihre Beziehungen zur Verteilung der Primzahlen.  Math. Z.  6  (1920),  no. 1-2, 11--51 ; Math. Z.  1  (1918),  no. 4, 357--376.
Here is an extract from the Zentralblatt review of Hecke's articles :

Übersetzt man den so gefundenen Sachverhalt in die Sprache der
  Formentheorie, so ergeben sich Sätze von folgender Art:
  Jede der Formen $x^2+y^2$ und
  $x^2−2y^2$ stellt unendlich viele
  Primzahlen dar, wenn man die Variabeln
  $x$, $y$ auf eine beliebigen
  Winkelraum einschränkt, welcher von
  zwei vom Nullpunkt der $x$−$y$-Ebene
  ausgehenden Halbstrahlen begrenzt
  wird. Überdies ist die Anzahl dieser
  Primzahlen unterhalb $t$ für $t \to
> \infty$ asymptotisch proportional der
  Grösse dieses Winkels, gemessen in
  einer auf die betreffende Form
  gegründeten Klein-Cayleyschen
  Massbestimmung.

