[PDF] Top 20 On Fermat’s equation over some quadratic imaginary number fields
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On Fermat’s equation over some quadratic imaginary number fields
... eigenforms over Q are just reductions of complex ...is imaginary quadratic, but ¸Sengün and Siksek [27] managed to circumvent this difficulty by assuming that the prime p is large ... See full document
16
Euler systems for modular forms over imaginary quadratic fields
... A number of previous works ([BD05], [How06], [Cas14]) have explored a rather different kind of Euler system attached to modular forms over an imaginary quadratic field, arising from Heegner ... See full document
43
On Lifting and Modularity of Reducible Residual Galois Representations Over Imaginary Quadratic Fields
... such representations where q = #F. This demonstrates that in general not all reducible representations τ can be modular (of a particular level and weight), as the number of such characteristic zero automorphic ... See full document
30
On approximations over ideal bases in quadratic number fields
... on fields, valuations, ideals, and quadratic forms, that will be subsequently ...The fields to be considered are quadratic number fields, ...2 over Q* distinction is to be ... See full document
140
On the asymptotic Fermat's Last Theorem over number fields
... the Fermat equation over number fields, with the earliest reference being to the work of Maillet ...(1897). Over a period of almost a century, number theorists have ... See full document
13
On Serre's uniformity conjecture for semistable elliptic curves over totally real fields
... curves over number fields, whose proofs make essential use of Merel’s ...a number field that does not contain the Hilbert class field of an imaginary quadratic field, then there ... See full document
8
Modular elliptic curves over real abelian fields and the generalized Fermat equation $x^{2\ell}+y^{2m}=z^p$
... lowering over totally real fields to study Diophantine ...representations over number fields of relatively high degree, and because we are aiming for a “clean” result without any ... See full document
30
Lattice methods for finding rational points on varieties over number fields
... is imaginary quadratic and O K is ...five number fields satisfying these conditions: Q( √ −1), Q( √ −2), Q( √ −3), Q( √ −7) and Q( √ ... See full document
109
On elliptic curves of prime power conductor over imaginary quadratic fields with class number one
... nine imaginary quadratic fields of class number one a result of Serre (1987) and Mestre-Oesterl´ e (1989), namely that if E is an elliptic curve of prime conductor then either E or a 2-, 3- or ... See full document
34
Overconvergent modular symbols over number fields
... the imaginary quadratic case, this interpolation property does not necessarily determine the distribution uniquely; we conclude by remarking on this lack of ... See full document
218
Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field
... called imaginary quadratic number fields and their corresponding sets of ...an imaginary quadratic number field may not always hold, the ideals of the ring of integers ... See full document
38
Modular symbols over number fields
... a number field, R its ring of integers. For some classes of fields, spaces of cusp forms of weight 2 for GL(2, K) have been computed using methods based on modular ...methods over Q to the ... See full document
148
Class Number Formula for Certain Imaginary Quadratic Fields
... Euler number E ( p − 1 ) / 2 in the case p ≡ 1 (mod 4 ) is the least positive residue mod p , and it a fortiori that it is not divisible by p, answering the question posed by Guy [3,B45] as ... See full document
6
The generalized Fermat equation over totally real number fields
... 3. Fermat wrote that had a marvellous proof of this which unfortu- nately was too large to fit in the ...by Fermat ever surfaced and the general consensus is that Fermat did not have a general proof ... See full document
135
p Tower Groups over Quadratic Imaginary Number Fields
... a quadratic imaginary number field has historically been one of the few exceptions to this ...be quadratic imaginary): • The work of Golod and Shafarevich [GS64] provided the first ... See full document
10
Observations on Ternary Quadratic Equation z2 = 82x2 +y2
... ternary quadratic homogeneous equation k ( x 2 y 2 ) bxy 4 k 2 2 z , (k, ,b 0) has been studied for its non-trivial integral ...ternary quadratic Diophantine equation of the form ... See full document
7
Torsion of elliptic curves over real quadratic fields of smallest discriminant
... of all K-rational points on E, together with the base point O, is an abelian group. He also conjectured that this group is finitely generated when K is the field Q of rational numbers. In 1922, Mordell proved this ... See full document
9
Representation of Algebraic Integers as Sum of Units over the Real Quadratic Fields
... of imaginary quadratic fields 𝑄(√𝑑), 𝑑 < 0, 𝑑 = −1, −2, −3 as sum of units of this field of certain repetition 𝑡, 𝑡 ≥ ...the imaginary fields in 𝑊 𝑡 ... See full document
5
Early Proofs of Fermat‟s Little Theorem and Applications
... Fermat‟s Little Theorem is one of the jewels of Number Theory and to mark the 400th anniversary of Fermat‟s ...de Fermat first revealed his ...of Fermat‟s Little ... See full document
6
Complex Number Theory without Imaginary Number (i)
... complex number, the length of i shown on vertical axis is equal to 1; it is a contradiction since value of imaginary number i is not ...complex number with other needs to multiply it by ... See full document
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