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Some new maps and ideals in classical Iwasawa theory with applications

David Solomon (2014)

Acta Arithmetica

We introduce a new ideal of the p-adic Galois group-ring associated to a real abelian field and a related ideal for imaginary abelian fields, Both result from an equivariant, Kummer-type pairing applied to Stark units in a ℤ p -tower of abelian fields, and is linked by explicit reciprocity to a third ideal studied more generally in [D. Solomon, Acta Arith. 143 (2010)]. This leads to a new and unifying framework for the Iwasawa theory of such fields including a real analogue of Stickelberger’s Theorem,...

Some new Results for Additive Self-Dual Codes over GF(4)

Varbanov, Zlatko (2007)

Serdica Journal of Computing

* Supported by COMBSTRU Research Training Network HPRN-CT-2002-00278 and the Bulgarian National Science Foundation under Grant MM-1304/03.Additive code C over GF(4) of length n is an additive subgroup of GF(4)n. It is well known [4] that the problem of finding stabilizer quantum error-correcting codes is transformed into problem of finding additive self-orthogonal codes over the Galois field GF(4) under a trace inner product. Our purpose is to construct good additive self-dual codes of length 13...

Some new sums related to D. H. Lehmer problem

Han Zhang, Wenpeng Zhang (2015)

Czechoslovak Mathematical Journal

About Lehmer’s number, many people have studied its various properties, and obtained a series of interesting results. In this paper, we consider a generalized Lehmer problem: Let p be a prime, and let N ( k ; p ) denote the number of all 1 ≤ a i ≤ p - 1 such that a 1 a 2 ⋯ a k ≡ 1 mod p and 2 ∣ a i + a ¯ i + 1 , i = 1 , ...

Some new transformations for Bailey pairs and WP-Bailey pairs

James Mc Laughlin (2010)

Open Mathematics

We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.

Some observations on the Diophantine equation f(x)f(y) = f(z)²

Yong Zhang (2016)

Colloquium Mathematicae

Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.

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