Characteristic functions and Bernoulli numbers
نویسندگان
چکیده
منابع مشابه
Mapping Class Groups, Characteristic Classes and Bernoulli Numbers
The mapping class group Γg of a closed, connected and oriented surface Sg of genus g is defined as the group of connected components of the group of orientation preserving diffeomorphisms of Sg. This group has been the object of many recent studies. Of particular interest are its finite subgroups; these are precisely the finite groups which occur as groups of symmetries of the surface Sg equipp...
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The three fundamental properties of the Bernoulli numbers, namely, the theorem of von Staudt-Clausen, von Staudt’s second theorem, and Kummer’s original congruence, are generalized to new numbers that we call generalized Bernoulli-Hurwitz numbers. These are coefficients of power series expansion of a higher genus algebraic function with respect to suitable variable. Our generalization strongly ...
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Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (modp), where p is an odd prime, x is a p-integral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=x ) (modp ); ∑(p−1)=2 x=1 (1=x ) (modp ); (p − 1)! (modp ) and Ar(m;p) (modp), where k ∈ {1; 2; : : : ; p− 1} and Ar(m;p) i...
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ژورنال
عنوان ژورنال: Journal of Multivariate Analysis
سال: 1972
ISSN: 0047-259X
DOI: 10.1016/0047-259x(72)90030-9