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Solving equations of signature with coefficients over number fields
Begum Gulsah Cakti, Erman Isik, Yasemin Kara +1
Using the modular method, we study solutions to the Diophantine equation over number fields. We first prove an asymptotic result for general number fields satisf…
On the growth of Tate-Shafarevich groups of -supersingular abelian varieties of -type over -extensions of number fields
Erman Isik, Antonio Lei
We study the boundedness of the Mordell-Weil rank and the growth of the -primary part of the Tate-Shafarevich group of -supersingular abelian varieties of -type w…
On Anticyclotomic Iwasawa Theory of Hecke Characters at Ordinary Primes
Erman Isik
In this article we study the Iwasawa theory for Hecke characters associated with CM abelian varieties and Hilbert modular forms at ordinary primes. We formulate and prove a result…
The growth of Tate-Shafarevich groups of -supersingular elliptic curves over anticyclotomic -extensions at inert primes
Erman Isik, Antonio Lei
Let be an elliptic curve defined over , and let be an imaginary quadratic field. Consider an odd prime at which has good supersingular reduction with $a…
On Modular Approach to Diophantine Equation over Number Fields
Erman Isik
Recent results of Freitas, Kraus, Sengun and Siksek give sufficient criteria for the asymptotic Fermat's Last Theorem to hold over various number fields. In this paper, we prove as…
On Ternary Diophantine Equations of Signature over Number Fields
Erman Isik, Yasemin Kara, Ekin Ozman
In this paper, we prove results about solutions of the Diophantine equation over various number fields using the modular method. Firstly, by assuming some standard mo…