An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces.
An alternative way to classify some Generalized Elliptic Curves and their isotopic loops
The Generalized Elliptic Curves are pairs , where is a family of triples of “points” from the set characterized by equalities of the form , where the law makes into a totally symmetric quasigroup. Isotopic loops arise by setting . When , identically is an entropic and is an abelian group. Similarly, a terentropic may be characterized by and is then a Commutative Moufang Loop . If in addition , we have Hall and is an exponent
An analog of crank for a certain kind of partition function arising from the cubic continued fraction
An analog of van der Corput's A⁴-process for exponential sums
An analogue in certain unique factorization domains of the Euclid-Euler theorem on perfect numbers.
An Analogue of Artin-Schreier Theorem.
An analogue of class-number in higher dimensions.
An analogue of Pfister's local-global principle in the burnside ring
Let be a Galois extension with Galois group . We study the set of -linear combinations of characters in the Burnside ring which give rise to -linear combinations of trace forms of subextensions of which are trivial in the Witt ring W of . In particular, we prove that the torsion subgroup of coincides with the kernel of the total signature homomorphism.
An Analogue of Stickelberger's Theorem for the Higher K-Groups.
An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.
An analogue of the Thue-Morse sequence.
An analogue of the Weierstrass ζ-function in characteristic p
An analogue of the Weil representation for G2.
An analysis of GCD and LCM matrices via the -factorization.
An analytic construction of degenerating curves over complete local rings
An analytic function and iterated integrals
An annihilator for the -Selmer group by means of Heegner points
Let be a modular elliptic curve, and let be an imaginary quadratic field. We show that the -Selmer group of over certain finite anticyclotomic extensions of , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic -extension of . This refines in the current contest a result of [1].
An Apéry-like difference equation for Catalan's constant.
An application of a formula of Western to the evaluation of certain Jacobsthal sums
An application of a lower bound for linear forms in two logarithms to the Terai-Jeśmanowicz conjecture