 About 1,800,000 results  books.google.com formula and Dirichlet's class number formula. In terms of Kummer's theory,
Dirichlet's formula is simply the limiting case as s\,\ of the generalization (2) of the
Euler product formula (1) when the divisors and prime divisors that occur in (2)
are ... 

 books.google.com 2T 'y The variational equation (A3.14) may be differentiated with respect to each
variable without losing its validity. For, as is easily seen, if a harmonic function is
O(6) uniformly in a given domain, the same is true of all its derivatives in each ... 

 books.google.com To prove the first formula, we substitute for C*(u) its expression as a definite
integral". We thus obtain  c. (owto" au ("oy"an cooo'd,  food. I (u–7)* '(ou)"~"
du T (k + 1) T(w) [" k+ u – 1 T(k+ p.)  C(T) (o–T) dr, which is the formula required. 

 books.google.com §6.5 is devoted to a derivation of the trace formula for Dirichlet's problem from
Theorem 6.4.6, which can be naturally regarded as a variant of the classical
Selberg trace formula. At the beginning of the section we prove a spectral trace
formula ... 

 books.google.com Theorem Dirichlet's Approximation Theorem Given any REAL NUMBER 0 and
any POSITIVE INTEGER N, there exist ... Dirichlet's BoxingIn Principle
DIRICHLET'S BOX PRINCIPLE Dirichlet's Formula If g is continuous and u, v > 0,
then t ... 

 books.google.com ... 104 Dini's formula, 241 Directional derivative, 160—61 Dirichlet, Peter Gustav
Lejeune, 40, 283 Dirichlet's conditions, 111, 132, 194 Dirichlet's formula, 138
Dirichlet's principle, 199, 201, 216 Dirichlet's problem, 98, 185, 186, 199 ff.;
exterior, ... 

 books.google.com Dirichlet's Vorlesungen iiber Zahlentheorie is one of the most important
mathematics books of the 19th century: the link ... to number theory today  but
also a lucid and thorough treatment of Dirichlet's class number formula for
quadratic forms. 

 books.google.com (In complex variable language, πK (s) has a simple pole at s = 1, and Dirichlet's
formula gives the residue.) The formula for the residue involves many of the
arithmetic quantities related to K, such as the class number, the discriminant, the
... 

 books.google.com so that G = G1+G2, and we apply the iterated integration formula to each of Gu
G2 We find that { dF*dG= I dF*dGi+ J ... On the other hand, we might have such
large estimates for Fv or Gv that the use of Dirichlet's formula proves wasteful. 

 books.google.com A Deformation of Dirichlet's Class Number Formula Takashi Ono Department of
Mathematics The Johns Hopkins University Baltimore, Maryland 1. Dirichlet's
Formula Let I be a prime of the form l=4N + 1, # be a primitive lth root of unity, ... 

 