Congruences for the Coefficients within a Generalized Factorial Polynomial
نویسندگان
چکیده
منابع مشابه
Congruences Involving Generalized Central Trinomial Coefficients
For integers b and c the generalized central trinomial coefficient Tn(b, c) denotes the coefficient of xn in the expansion of (x2 + bx + c)n. Those Tn = Tn(1, 1) (n = 0, 1, 2, . . . ) are the usual central trinomial coefficients, and Tn(3, 2) coincides with the Delannoy number Dn = ∑n k=0 (n k )(n+k k ) in combinatorics. We investigate congruences involving generalized central trinomial coeffic...
متن کاملGeneralized Factorial Functions and Binomial Coefficients
Let S ⊆ Z. The generalized factorial function for S, denoted n!S , is introduced in accordance with theory already established by Bhargava ([4]). Along with several known theorems about these functions, a number of other issues will be explored. This Thesis is divided into 4 chapters. Chapter 1 provides the necessary definitions and offers a connection between the generalized factorial function...
متن کاملOn congruences for the coefficients
1997 2 Kevin Lee James On con gruences for the coefficients of modular forms and some applications (Under the direction of Andrew Granville) In this dissertation, we will study two different conjectures about elliptic curves and modular forms. First, we will exploit the theory developed by Shimura and Waldspurger to address Goldfeld's conjecture which states that the density of rank zero curves...
متن کاملBinomial and factorial congruences for Fq[t]
We present several elementary theorems, observations and questions related to the theme of congruences satisfied by binomial coefficients and factorials modulo primes (or prime powers) in the setting of polynomial ring over a finite field. When we look at the factorial of n or the binomial coefficient ‘n choose m’ in this setting, though the values are in a function field, n and m can be usual ...
متن کاملConnection Coefficients Between Generalized Rising and Falling Factorial Bases
Let S = (s1, s2, . . .) be any sequence of nonnegative integers and let Sk = ∑k i=1 si We then define the falling (rising) factorials relative to S by setting (x)↓k,S= (x−S1)(x−S2) · · · (x−Sk) and (x)↑k,S= (x+S1)(x+S2) · · · (x+Sk) if k ≥ 1 with (x)↓0,S= (x)↑0,S= 1. It follows that {(x)↓k,S}k≥0 and {(x)↑k,S}k≥0 are bases for the polynomial ring Q[x]. We use a rook theory model due to Miceli an...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 2002
ISSN: 0035-7596
DOI: 10.1216/rmjm/1030539622