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Showing 1 to 20 of 35 for “"congruences"”.
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Generalized Kummer congruences and Iwasawa invariants
We obtain the following generalization of the Kummer congruence: $$G\sb{c}(j,\chi,n) = -\left\lbrack{p\sp{-1}\Delta\sb{\rm c}\atop j}\right\rbrack {1\over n}(1 - \chi\omega\sp{-n}(p)\ p\sp{n-1}) B\sb{n,\chi\omega\sp{-n}}\in\doubz\sb{p}\lbrack\chi\rbrack ,$$where $B\sb{n,\chi}$ is the generalized …
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On Homogeneous Diagonal Congruences of Odd Degree
Made available in DSpace on 2014-12-09T22:17:36Z (GMT). No. of bitstreams: 1 6706692.pdf: 4255711 bytes, checksum: 4b018e9b8a1387099d61fcbe54597957 (MD5) Previous issue date: 1966
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Congruences and amalgamation in small lattice varieties
When it became apparent that many varieties of algebras do not satisfy the Amalgamation Property, George Grätzer introduced the concept of an amalgamation class of a variety . The bulk of this dissertation is concerned with the amalgamation classes of residually small lattice varieties, with an …
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Congruences on lattices (with application to amalgamation)
We present some aspects of congruences on lattices. An overview of general results on congruence distributive algebras is given in Chapter 1 and in Chapter 2 we examine weak projections; including Dilworth's characterization of congruences on lattices and a finite basis theorem for lattices. The …
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Congruences for the Coefficients of Weakly Holomorphic Modular Forms
… the theory of modular forms to establish linear congruences for the partition function and for traces of singular moduli. In each case, the values of the given arithmetic function appear as the Fourier coefficients of a weakly holomorphic modular form. We show that similar congruences exist for …
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Computing congruences and endomorphisms for algebras of type (2m, 1n)
… O objetivo da package CREAM (Algebra CongRuences, Endomorphisms and AutomorphisMs) é resolver esta situação implementando algoritmos eficientes para calcular congruências, endomorfismos e automorfismos de álgebras do tipo (2m, 1 n). Vários algoritmos gerais (como em [15]) serão …
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Congruences in modular, Jacobi, Siegel, and mock modular forms with applications
We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the …
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L-invariants and congruences for Galois representations of dimension 3, 4, and 8
… 𝘬 > 2. In the second half we will establish congruences between 𝘱-adic 𝘓-functions. In the late 1990s, Vatsal showed that a congruence modulo 𝘱 ᵛ between two newforms implied a congruence between their respective 𝘱-adic 𝘓-functions. We shall prove an analogous statement for both the double …
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ΣΥΜΒΟΛΗ ΣΤΗ ΜΕΛΕΤΗ ΤΩΝ W-ΣΜΗΝΩΝ ΣΤΑ ΠΛΑΙΣΙΑ ΤΗΣ ΠΡΟΒΟΛΙΚΗΣ ΔΙΑΦΟΡΙΚΗΣ ΓΕΩΜΕΤΡΙΑΣ
… IS DEVOTED TO THE STUDY OF COMPLEXES AND CONGRUENCES OF STRAIGHT LINES IN THE REAL PROJECTIVE SPACE P3. IN CHAPTER I WE PRESENT, FOR THE MOST PART, KNOWN RESULTS. CHAPTER II IS CONCERNED WITH THE M-TH OSCULATING SPACE IN A STRAIGHT LINE OF CONGRUENCE. IN CHAPTER III WE PROVE THAT IN P3 …
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L-functions and J-spectra
… series by Dirichlet characters. We first explain congruences of these twisted Eisenstein series of level Γ_1(N) and character χ via the Dieudonné theory of height 1 formal groups and formal A-modules and their finite subgroups. Our approach is based on Katz’s algebro-geometric explanation of …
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Covering Systems
A collection of congruences with distinct moduli, each greater than 1, such that each integer satisfies at least one of the congruences, is said to be a set of covering congruences, or covering system. A famous conjecture of Erdos from 1950 states that the least modulus of a covering system can be …
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Iwasawa theory over solvable three-dimensional p-adic Lie extensions
… factoring through G∞ using p-adic congruences, and then (2) show for each motive that the abelian fragments satisfy these congruences. This thesis provides a complete answer to the first task (1), in the specific situation where the pro-p-group G∞ has dimension ≤ 3 and is …
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p-adic L-functions and the Geometry of Hida Families
… a converse to a result of Vatsal relating congruences between eigenforms to their algebraic special $L$-values and then $p$-adically interpolating congruences using formal models. These methods should extend to the entire eigencurve.</p>
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Covering Systems of Polynomial Rings Over Finite Fields
… every integer belonged to a certain system of congruences with distinct moduli. He called such systems of congruences covering systems. Utilizing his covering system, he disproved a conjecture of de Polignac asking, “for every odd k, is there a prime of the form 2n + k?” Examples of covering …
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Problems in number theory and hyperbolic geometry
… concerning the existence of Ramanujan-type congruences for a class of eta quotients. Specifically, we consider a class of generating functions analogous to the generating function of the partition function and establish a bound on the primes ℓ for which their coefficients c(n) obey …
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Explicit moduli spaces for curves of genus 1 and 2
… moduli surfaces $Z_{N,r}$ which parametrise $N$-congruences of elliptic curves which raise the Weil pairing to a power of $r$. We first study the birational geometry of the surfaces $Z_{N,r}^{\text{sym}}$ which arise as quotients of the surfaces $Z_{N,r}$ by the involution swapping the roles of …
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Behavior of partition values modulo powers of primes
… years ago, Ramanujan proved the celebrated congruences for <italic>p(n)</italic> which bear his name. For example, he proved, for all <italic>n</italic>, that <italic>p(5n + 4) == 0 mod 5</italic>. Work of Ono and others over the last ten years reveals the extent to which …
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The annihilation graphs of commutator posets and lattices
… products of ideals). The intermediate level of congruences of any algebraic structure admitting a "good" theory of commutators is also considered.
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Partition asymptotics; zeros of zeta functions; and Apéry-like numbers
… to the irrationality of _(3) satisfy Lucas congruences. Our main result is to prove corresponding congruences for all known sporadic Apéry-like sequences. In several cases, we are able to employ approaches due to McIntosh, Samol-van Straten and Rowland-Yassawi to establish these congruences. …
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