Motivation for weight (0, 0) over imaginary quadratic fields
Euler systems for modular forms over imaginary quadratic fields
... groups: motivation Our final result on bounding Selmer groups will be an application of Theorem ...f over the Z 2 p -extension of K; these ideas play no role in the proofs, but serve to motivate our choice ...
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On congruences of modular forms over imaginary quadratic fields
... Π 0 of GSp(4, A Q ), such that R 0 | I p ∼ = τ p , for all p ∈ ...GL(2) over an imaginary quadratic ...general fields, and to more general automorphic ...
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Modularity of abelian surfaces over imaginary quadratic fields
... Introduction One of the crowning achievements of mathematics in the 20th century was the proof of Fermat’s last theorem. Whilst the result itself is of huge importance in the mathematical community for historical ...
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On Fermat’s equation over some quadratic imaginary number fields
... On the other hand, modularity of elliptic curves over number fields with complex embeddings is highly conjectural. For general number fields, ¸Sengün and Siksek [27] proved an asymptotic version of Fermat’s Last ...
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p Tower Groups over Quadratic Imaginary Number Fields
... find fields with large p-rank for p = 2 by the classical genus theory of Gauss, and for other primes by the work of Yamamoto [Ya70], Mestre [Me83], and Buell [Bu76], among ...(∞) over a quadratic ...
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On Lifting and Modularity of Reducible Residual Galois Representations Over Imaginary Quadratic Fields
... representations over imaginary quadratic fields considered in section ...an imaginary quadratic field which were made in section ...
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Class Number Formula for Certain Imaginary Quadratic Fields
... Thus deducing a congruence of an Euler number through the class number (or one of its equivalent forms) is in the reverse direction, i. e. rather similar to the related problem of Chowla which asks for an elementary ...
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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 ...
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Universal adelic groups for imaginary quadratic number fields and elliptic curves
... number fields have isomorphic rings of integers, then they are obviously isomorphic, as K is the field of fractions of its ring of ...number fields of the same degree can have the same discriminant, or how ...
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Lectures on the Dirichlet Class Number Formula for Imaginary Quadratic Fields. Tom Weston
... We give a different, and somewhat better, proof of this proposition in Exer- cises 4.5 and 4.6. 3. Euler products The Dirichlet series of interest in number theory have an additional special property: they have ...
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On approximations over ideal bases in quadratic number fields
... The work is subdivided into four chapters, of which the first, mainly expository in character, lay down the foundations for the investigation proper which follows. Chapters II and III concern exclusively the cases of ...
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GAUSS' CLASS NUMBER PROBLEM FOR IMAGINARY QUADRATIC FIELDS
... If the Birch- Swinnerton-Dyer conjecture is true for a suitable fixed elliptic curve of rank g = 3, then this theorem effectively solves the general Gauss class number problem; i.e., t[r] ...
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Solving $X^{q+1}+X+a=0$ over Finite Fields
... under a MCM polynomial and to find preimages of an element in F 2 n under a Dickson polynomial. By completely solving these two independent problems, they explicitly calculated all possible zeros in F 2 n of P a (X ), ...
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IMAGINARY QUADRATIC FIELDS WHOSE EXPONENTS ARE LESS THAN OR EQUAL TO TWO
... IMAGINARY QUADRATIC FIELDS WHOSE EXPONENTS ARE LESS THAN OR EQUAL TO TWO Kenichi SHIMIZU ...an imaginary quadratic field to have exponent less than or equal to ...
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A B C D E F G H I J K L Nonsalary Benefits FY % $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0 $0
... Name Position Funding Source Salary (09/01/14) Percentage Salary Increase Over FY 2014 Bonuses Benefits Allowance Car Allowance Other Compensation Total Compensation Explanat[r] ...
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in (a)(1) institutional dollars $ 0 $ 59,183 $ 0 $ 0 Student Waivers and Refunds $ 0 $ 0 $ 0 $ 0 $ 0 $ 0 $ 0 $ 1,185,101 $ 0 $ 104,270 $ 0 $ 0
... 2 Including costs or expenses related to the disinfecting and cleaning of dorms and other campus facilities, purchases of personal protective equipment (PPE), purchases of cleaning supplies, adding personnel to increase ...
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ATX Client Write-Up (ATX Inc.) 0% 0% 0% 1% 0% 0% 0% Bill.com 0% 0% 0% 0% 1% 0% 0%
... 1% 0% 1% 0% 4% Exhibit 2: Tax Preparation Software The top section of the following chart lists the percentage of firms using each product in the seven revenue categories tracked by the MAP ...
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Difference (Remaining Funds) $0 $0 $0 $0 $0 $0
... High - District Totals 1,407 1,266 1,087.32 85.86 % 150 1,221 86.23 % Other - ESE, etc 0 0 0.00 0.00 % 0 0 0.00 % 5,376 5,104 4,578.21 89.70 % 392 5,225 95.07 % Combination schools are ...
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Always Frequently Sometimes Rarely Never N/A 13 (100%) 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%)
... * Professor Mueller effectively used the written material contained in the text to enhance the class reading and writing techniques. * He has helped me discover what writing and reading are all about. He challenged me to ...
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discriminant ) of the quadratic equation ax 2bxc 0 is given by
... New QMaths 11B CD-ROM Extra material The discriminant A quadratic equation may have rational or irrational roots. In some cases there is only one root. The quadratic equation x 2 + x + 5 = 0 has no ...
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