Congruences involving Bernoulli polynomials

作者：Sun Zhi Hong^*

来源：Discrete Mathematics, 2008, 308(1): 71-112.

DOI：10.1016/j.disc.2007.03.038

• congruence
• Bernoulli polynomial
• p-regular function
• class number
• Euler number

Let {B-n (x)} be the Bernoulli polynomials. In the paper we establish some congruences for B-j(x) (mod p(n)), where p is an odd prime and x is a rational p-integer. Such congruences are concerned with the properties of p-regular functions, the congruences for h(-sp) (mod p) (s = 3, 5, 8, 12) and the sum Sigma(k equivalent to r) (mod m) ((p)(k)), where h(d) is the class number of the quadratic field Q(root d) of discriminant d and p-regular functions are those functions f such that f(k) (k = 0, 1,...) are rational p-integers and Sigma(n)(k=0)((n)(k))(-1)(k) f(k) equivalent to 0 (mod p(n)) for n = 1, 2, 3,.... We also establish many congruences for Euler numbers.

• 出版日期2008-1-6
• 单位淮阴师范学院