[PDF] Top 20 Ramanujan type congruences modulo powers of 5 and 7
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Ramanujan type congruences modulo powers of 5 and 7
... Recently, by following the strategy of Hirschhorn and Hunt [5], Wang [11, 12] established several infinite families of congruences modulo powers of 5 for b5 n and B5 n.. In recent days, [r] ... See full document
17
Induction of Transformation and p53-Dependent Apoptosis by Adenovirus Type 5 E4orf6/7 cDNA
... from 5 g of RNA by using Rous-associated virus-2 (RAV) reverse transcriptase (TaKaRa Biomedicals), and then E4orf6 and E4orf6/7 were specifically amplified by Expand High Fidelity (Boehringer Mannheim) ... See full document
9
Some congruences on q Franel numbers and q Catalan numbers
... 8. G. Olive, Generalized powers, Amer. Math. Monthly, 72 (1965), 619-627. 9. H. Pan, A q-analogue of Lehmer’s congruence, Acta Arith., 128 (2007), 303-318. 10. Z.-W. Sun, Congruences for Franel numbers, ... See full document
9
Further Identities Of Rogers-Ramanujan Type
... The transformation (1.1) is a limiting case of a q-analogue of the Kummer Thomae-Whipple formula (see [5] P-72, Equation 3.2.7) or (see [7] p-40, Eq. (6.1.2)). The transformation (1.2) is found in [10] and ... See full document
10
The ABC of Community law. Third edition. European Documentation 1991
... CONTENTS INTRODUCTION 5 THE 'CONSTITUTION' OF THE EUROPEAN COMMUNITY 7 STRUCTURE OF THE COMMUNITY Tasks - Powers - Legal character FUNDAMENTAL VALUES OF THE COMMUNITY Peace - Unity - Equ[r] ... See full document
57
Some Connections Between Primitive Roots and Quadratic Non-Residues Modulo a Prime
... roots modulo a prime is an funda- mental problem in number theory, with major applications in ...non-residues modulo a prime is another interesting problem in number ...roots modulo a prime and ... See full document
6
On the Fine-Structure of Regular Algebra
... early result by Redko [28] rules out any finite equational axiomatisation. Salomaa [29] gave two axiom systems based on inference rules which, essentially, encode Arden’s rule from formal language theory. He proved ... See full document
33
Ramanujan graphs in cryptography
... = 5 and l = 13, and describes how the same can be done in ...Section 7 we give an overview of how Strong Approximation plays a role in proving the isomorphisms and the connectedness and Ramanujan ... See full document
33
The Nested Periodic Subspaces: Extensions of Ramanujan Sums for Period Estimation
... All these differences when put together, result in significantly better accuracies and much simpler algorithmic complexity for integer period estimation, as will be seen in Sec. 6.4. Before proceeding, we will show a ... See full document
211
On a family of semigroup congruences
... The above figure is obtained by putting together all the diamonds and recursive relations proved in the earlier sections of the present chapter. One can prove each of the diamonds on P(n) using Corollary 7:2.8, ... See full document
218
On Identities Of Rogers-Ramanujan Type
... The transformation (2.1) is a limiting case of a q-analogue of the Kummer Thomae-Whipple formula (see [5] P-72, Equation 3.2.7) or (see [7] p-40, Eq. (6.1.2)). The proof of transformation (2.2) is found in ... See full document
10
1974 conjecture of Andrews on partitions
... S 5 = {π + 7+ 6+x + y : (x,y) = all possible pairs of 1,2, 3, 4,9, = all possible pairs of 1, 2, 10, 11, 12 except (9, 4)} 3, 4, 9,10, 11, 12 except (9, 4)} ∪{π +13 +(13 −x 1 ) +··· 4th stage of S 3 = {π + ... See full document
8
Ramanujan-style congruences of local origin
... condition 7 ∤ n may appear to be a problem, but, as pointed out by a referee, this can be fixed by a trick involving a character ...conductor 7. Then χ(n)b n ≡ χ(n)σ 5 (n) for em all integers 1 ≤ n ≤ ... See full document
12
The ABC of Community law. Fourth edition. European Documentation 1994
... CONTENTS INTRODUCTION 5 THE 'CONSTITUTION' OF THE EUROPEAN COMMUNITY 7 • STRUCTURE OF THE COMMUNITY Tasks - Powers - legal character • FUNDAMENTAL VALUES OF THE COMMUNITY Peace- Unity- E[r] ... See full document
74
The Rogers Ramanujan Identities
... Remarks 2: C 1 n C n , (6) i.e., the number of partitions of n into parts not less than 2 and with minimal difference 2 is equal to the number of partitions of n into parts of the forms 5m + 2 and 5m + 3. ... See full document
10
Eisenstein Congruences for SO(4, 3), SO(4, 4), Spinor, and Triple Product L-values
... apparent congruences of the right shape, showing that they hold for p ≤ ...the congruences for all ...these congruences appear in the numerators of certain ratios of critical spinor ... See full document
36
Congruences for l regular overpartition for lϵ {5, 6, 8}
... CONGRUENCES FOR `−REGULAR OVERPARTITION FOR ` ∈ {5, 6, 8} Nipen Saikia and Chayanika Boruah Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791 112, Arunachal Pra[r] ... See full document
14
On congruences of automata defined by directed graphs
... of the original graph labeling. Our paper contributes to this direction and con- tinues the investigation initiated in [5], where the concept of a graph algebra has been used in order to define finite state ... See full document
16
Divergence and convergence in the federal judicial system
... non-judicial powers in their personal capacity (Grollo v Palmer (1995) 184 CLR 348, Hilton v Wells (1985) 157 CLR 57, Wilson v Minister for Aboriginal and Torres Strait Islander Affairs (1996) 189 CLR 1) and that ... See full document
76
Some theorems on the explicit evaluation of Ramanujan's theta functions
... Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan’s formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class ... See full document
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