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Information Seminar Paper

Title

THE LANG-TROTTER CONJECTURE

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Abstract

 FOR A PRIME P AND FIXED INTEGERS A AND B, LET N (P) BE THE NUMBER OF SOLUTIONS (X, Y) OF THE CUBIC Y2=X3+AX+B OVER THE FINITE FIELD FP AND LET A (P) =P − N (P). IN 1976, SERGE LANG AND HALE TROTTER FORMULATED A CONJECTURE REGARDING THE DISTRIBUTION OF PRIMES P FOR WHICH A (P) =A FOR A FIXED INTEGER A. THIS CONJECTURE IS WIDELY OPEN. IN THIS TALK WE GIVE AN EXPOSITION OF THIS CONJECTURE AND DESCRIBE SOME OF THE WORK DONE IN THIS TOPIC OVER THE LAST FEW DECADES. WE ALSO REPORT ON OUR RECENT JOINT WORK WITH JAMES PARKS (KTH ROYAL INSTITUTE OF TECHNOLOGY-SWEDEN) ON A VERSION OF THIS CONJECTURE FOR TWO CUBICS (ELLIPTIC CURVES).

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  • Cite

    APA: Copy

    Akbary, Amir. (2016). THE LANG-TROTTER CONJECTURE. ANNUAL IRANIAN MATHEMATICS CONFERENCE. SID. https://sid.ir/paper/938915/en

    Vancouver: Copy

    Akbary Amir. THE LANG-TROTTER CONJECTURE. 2016. Available from: https://sid.ir/paper/938915/en

    IEEE: Copy

    Amir Akbary, “THE LANG-TROTTER CONJECTURE,” presented at the ANNUAL IRANIAN MATHEMATICS CONFERENCE. 2016, [Online]. Available: https://sid.ir/paper/938915/en

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