A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Congruence classes in M3(Fq)(q even)

2002
*
Discrete Mathematics
*

*In*dimensions 2 and 3, the sizes of the

*congruence*

*classes*of matrices over a ÿnite ÿeld of characteristic 2 are determined. ... This complements the authors' earlier solution of the corresponding problem

*in*odd characteristic. ... The sizes of the

*congruence*

*classes*

*in*M 2 (F

*q*) (

*q*odd) are given

*in*Table 1 . Theorem 2. The sizes of the

*congruence*

*classes*

*in*M 2 (F

*q*) (

*q*

*even*) are given

*in*Table 2 . ...

##
###
Congruence classes in M3(Fq) (q odd)

2000
*
Discrete Mathematics
*

Over a ÿnite ÿeld, these representatives then enable us very easily to determine the sizes of the various

doi:10.1016/s0012-365x(99)00366-0
fatcat:whakndxx3fcqrev72qvtumh4vu
*congruence**classes*. ...*In*dimensions 2 and 3, matrices over a ÿeld of characteristic = 2 are classiÿed up to*congruence*by means of certain representatives which are sums of diagonal and antisymmetric matrices. ... The sizes of the*congruence**classes**in*M 2 (F*q*) (*q*odd) are given by: Representative Stabilizer |*Class*| 1 O 2; 1 2*q*(*q*− 1)(*q*+ (− )) 1 ÿ −ÿ SO 2;*q*(*q*− 1)(*q*+ (− )) 0 ±1 c d 1 2 (*q*2 − 1) 1 −1 0 ± ...##
###
Triple product p-adic L-function attached to p-adic families of modular forms
[article]

2019
*
arXiv
*
pre-print

We generalize his result

arXiv:1909.03165v2
fatcat:2rq33owoonahxn7cr64byhyhzi
*in*the unbalanced case and construct a three-variable triple product p-adic L-function attached to a primitive Hida family and two more general p-adic families of modular forms ... Let Ω*FQ*1 be the canonical period defined*in*Definition 3.3.4 and E*FQ*1 (Π*Q*,p ) be the modified p-Euler factor defined*in*(3.4.1). Our main theorem is as follows. Main Theorem. ... We put (π ′ 1 , π ′ 2 , π ′ 3 ) = (π*FQ*1 ⊗(χ*Q*) A , π G (2) (m2) , π G (3) (*m3*) ). The following proposition is proved*in*[Hsi17, Proposition 6.12]. Proposition 5.1.4. ...##
###
A Fractal-Like Algebraic Splitting of the Classifying Space for Vector Bundles

1988
*
Transactions of the American Mathematical Society
*

The pieces

doi:10.2307/2001182
fatcat:po7umsmuyjhifn4uu6l7ougaoa
*in*the splittings are finite, and the grading extends that of H*n2S3 which splits it into Brown-Gitler modules. ... There are fractal A-algebra maps*fq*: Bo -* B0 for*q*> 1 satisfying: (1) Each*fq*(ui) is an indecomposable*in*dimension i + 2m^+*q*, and thus*fq*is a monomorphism. (2)*fq*(Bn)EBn+1. PROOF. ...*In*this case, clearly*fq*(pdl) = gq(pdi), so we only need show that p(di+2m+*q*) -gqdz = 0. ...##
###
A fractal-like algebraic splitting of the classifying space for vector bundles

1988
*
Transactions of the American Mathematical Society
*

The pieces

doi:10.1090/s0002-9947-1988-0940211-9
fatcat:st3hzkriujeu3m6roqlbpw72bi
*in*the splittings are finite, and the grading extends that of H*n2S3 which splits it into Brown-Gitler modules. ... There are fractal A-algebra maps*fq*: Bo -* B0 for*q*> 1 satisfying: (1) Each*fq*(ui) is an indecomposable*in*dimension i + 2m^+*q*, and thus*fq*is a monomorphism. (2)*fq*(Bn)EBn+1. PROOF. ...*In*this case, clearly*fq*(pdl) = gq(pdi), so we only need show that p(di+2m+*q*) -gqdz = 0. ...##
###
Involutory elliptic curves over $\mathbb{F}_q(T)$

1998
*
Journal de Théorie des Nombres de Bordeaux
*

The author, being supported by CICMA

doi:10.5802/jtnb.221
fatcat:a3g4j4nikvdy7lgipelr7bndw4
*in*form of a post-doc position at Concordia University and McGill University, wishes to express his gratitude to all three institutions. ... Suppose that*q*is*even*and n = [m with (1, m) = 1 and deg(m) > 1. Write m = m2m1 with m1, m2 E*Fq*[T], where ml is square- free. ... It is given on (resp. rm for some*q*E F:. From this it is obvious that Wml Wm2 = with*m3*= (ml-. ...##
###
Lectures on Applied ℓ-adic Cohomology
[article]

2019
*
arXiv
*
pre-print

For any squarefree integer

arXiv:1712.03173v3
fatcat:g6yaohxdzzakxlq6egz6znomka
*q*, let a*q*(mod*q*) be the unique*congruence**class*modulo*q*such that ∀p|*q*, a*q*≡ a p (mod p);*in*particular a*q*∈ (Z/qZ) × . ... a set of integers has finite or infinite intersection with some*congruence**class*. ...*In*[FM98] , this was shown to hold more generally for the trace functions K(x) = e*q*(x −k + ax), a ∈ F*q*, k 1. (2) For more general trace functions, the first condition*in*(16.10) and (16.13) can be ...##
###
Quaternions and Projective Geometry

1903
*
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences
*

Ml5

doi:10.1098/rsta.1903.0018
fatcat:n46kmam63vdrnifdbky5cicb3a
*M3*and*M3*. ... The type of a function of this*class*I4 is*fq*(a d d 'd ") = a (a*q*d ' a ") + a ") + a" (ada'q)*in*which a, a , a"and d "are arbitrary quaternions. ... Dividing each member of the identities by (abed), we obtain the biquadratics and J (*q*),J' (*q*), J " (*q*),J' n (g), of the fourth, third, second and first ord*in**q*, are the invariants of f( p*q*) considered ...##
###
On Ree's Series of Simple Groups

1966
*
Transactions of the American Mathematical Society
*

Condition I implies that

doi:10.2307/1994333
fatcat:srzfyld2pjdplewilnehdpa2q4
*q*= 4 + e (mod 8) where e = + 1. IV. If denotes a cyclic subgroup of order (*q*+ e)/2*in*L, then the normalizer NC((R0}) of any subgroup of is contained*in*... For some element J of order 2 (an "involution")*in*G, the centralizer CG(J) of J*in*G is the direct product of and L where L is isomorphic to the linear fractional group LF(2,*q*). ... If then £¡ has multiplicity m¡*in*0, 2 :£ 1 + m2 +*m3*+ m4 and 2 ;£ 1 -m2 +*m3*-m4. Thus 1 ^*m3*; as £3 has degree <j3, 9 = Çx + ¿3. Thus [13] this action is doubly transitive. ...##
###
On Ree's series of simple groups

1966
*
Transactions of the American Mathematical Society
*

Condition I implies that

doi:10.1090/s0002-9947-1966-0197587-8
fatcat:zhhf44sl3bcoznl4xdzyyrgc44
*q*= 4 + e (mod 8) where e = + 1. IV. If denotes a cyclic subgroup of order (*q*+ e)/2*in*L, then the normalizer NC((R0}) of any subgroup of is contained*in*... For some element J of order 2 (an "involution")*in*G, the centralizer CG(J) of J*in*G is the direct product of and L where L is isomorphic to the linear fractional group LF(2,*q*). ... If then £¡ has multiplicity m¡*in*0, 2 :£ 1 + m2 +*m3*+ m4 and 2 ;£ 1 -m2 +*m3*-m4. Thus 1 ^*m3*; as £3 has degree <j3, 9 = Çx + ¿3. Thus [13] this action is doubly transitive. ...##
###
On Inverses of Permutation Polynomials of Small Degree over Finite Fields
[article]

2018
*
arXiv
*
pre-print

*In*this list, the explicit inverse of a

*class*of fifth degree PPs is our main result,which is obtained by using some

*congruences*of binomial coefficients, the Lucas' theorem, and a known formula for the ... Permutation polynomials (PPs) and their inverses have applications

*in*cryptography, coding theory and combinatorial design. ... If i is

*even*, then r i + 2j is

*even*, and so the coefficients of odd powers of x

*in*(6) are all 0. Also note k(

*q*− 1) + (

*q*− 2) is odd. We have b i,

*q*−2 = 0. ...

##
###
Equations and monoid varieties of dot-depth one and two

1994
*
Theoretical Computer Science
*

*In*this paper, we first simplify the infinite defining sequence of equations for VI ,m given

*in*[S]. ... For m > 1, a sequence of equations satisfied

*in*(but not necessarily complete for) V2,m is given. Parts of the present paper are also to be published

*in*[S]. ... Let

*m3*1. ...

##
###
Matrix representatives for three-dimensional bilinear forms over finite fields

1998
*
Discrete Mathematics
*

If ~ is symmetric or alternating, then explicit normal forms for the

doi:10.1016/s0012-365x(97)00183-0
fatcat:j4sqmzf3svhuph6r4myd26cdwq
*congruence**classes*over various fields are well known, but this is not the case for general asymmetric forms. ... Therefore, = {(aij) E*M3*(K) l a12 = a13 = a21 = a31 = 0}. Lemma 6. ...##
###
The cusp amplitudes and quasi-level of a congruence subgroup of SL2 over any Dedekind domain

2012
*
Proceedings of the London Mathematical Society
*

We study cusp amplitudes and the level of a (

doi:10.1112/plms/pdr071
fatcat:vohclabyhfbg7jvxeqztaklayi
*congruence*) subgroup of SL_2(D) for any Dedekind domain D, as ideals of D.*In*particular, we extend a remarkable result of Larcher. ... We extend some algebraic properties of the classical modular group SL_2(Z) to equivalent groups*in*the theory of Drinfeld modules,*in*particular properties which are important*in*the theory of modular ...*In*addition ql(∆(*Q*)) =*Q*, by [*M3*, Theorem 3.8] . Part (iii) follows. Suppose that l(∆(*Q*)) = (f ). ...##
###
The Eisenstein ideal and Jacquet-Langlands isogeny over function fields
[article]

2015
*
arXiv
*
pre-print

Let p and

arXiv:1306.3632v3
fatcat:bpbsap4kqjg2bmamabfi2tkhdq
*q*be two distinct prime ideals of F_q[T]. ... Our results are stronger than what is currently known about the analogues of these problems over*Q*. ... Part of this work was carried out while the first author was visiting Taida Institute for Mathematical Sciences*in*Taipei and National Center for Theoretical Sciences*in*Hsinchu. ...
« Previous

*Showing results 1 — 15 out of 80 results*