|
| Assoc. Prof. Dr. Ahmet TEKCAN |
Address: Uludag University , Faculty of Arts & Science , Department of Mathematics , Görükle , 16059, Bursa – TÜRKİYE
e-mails : tekcan@uludag.edu.tr , tekcan77@gmail.com
http: http://matematik.uludag.edu.tr/AhmetTekcan.htm
Office: + 90 (224) 294 17 51
Fax: + 90 (224) 294 18 98
Room: B-216
1) PERSONAL INFORMATION:
Birth date: 17 November 1977
Birthplace: Kayseri - TÜRKİYE
Citizenship: Turkish
Language: Turkish (native), English (advanced)
Married: 28 April 2001
Children: Melisa Yaren ( 28 June 2002 ), Ahmet Kağan ( 25 April 2008 )
2) EDUCATIONS:
3) ACADEMIC PROMOTIONS:
4) THESIS COMPLETED:
5) MATHEMATICS SUBJECT CLASSIFICATION 2000:
11Bxx |
Sequences and sets |
11B37, 11B39, 11B50 |
11-xx |
Number theory |
11A55, 11D25, 11D70, 11E11, 11E15, 11E16, 11E18, 11E25, 11F03, 11F22, 11G05, 11G07, 11G16, 11G20, 11J70 |
11Dxx |
Diophantine equations |
11D04, 11D09, 11D25, 11D41, 11D68, 11D72, 11D85 |
11Exx |
Forms and linear algebraic groups |
11E04, 11E08, 11E12, 11E16, 11E25, 11E39, 11E76. |
11Fxx |
Discontinuous groups and automorphic forms |
11F03, 11F11, 11F23, 11F27, 11F30. |
11Gxx |
Arithmetic algebraic geometry |
11G05, 11G07, 11G16, 11G30, 11G40, 11G50. |
57Mxx |
Low-dimensional topology |
57M05, 57M07, 57M10, 57M12. |
6) RESEARCH AREAS:
1 |
COVERING SPACES |
Covering spaces, universal, regular and Galois covering spaces, automorphism groups of covering spaces, fundamental group, Riemann surfaces, covering of Riemann surfaces. |
2 |
DISCRETE GROUPS |
Discrete groups, modular and extended modular group, special congruence subgroups, signature of the special and principal congruence subgroups. |
3 |
BINARY QUADRATIC FORMS |
Quadratic forms, cycle of forms, equivalence of forms, representation of positive integers by quadratic forms, theta series and Eisenstein series associated positive quadratic forms, ternary forms, Hermitian forms, representation of integers by Hermitian forms, cusp form, modular form. |
4 |
IDEALS |
Quadratic ideals, primitive ideals, cycles of ideals, ambiguous ideals, equivalence of ideals, relationship between ideals and quadratic forms, quadratic irrationals. |
5 |
ELLIPTIC CURVES |
Elliptic curves over finite fields, rational points on elliptic curves, rank of elliptic curves, torsion groups of elliptic curves, group structure of elliptic curves. |
6 |
ELLIPTIC DIVISIBILITY SEQUENCES |
Elliptic divisibility sequences, the connection between elliptic curves and elliptic divisibility sequences, elliptic divisibility sequences and Fibonacci and Lucas sequences. |
7 |
EQUATIONS |
Pell and Diophantine equations and their integer solutions, recurrence relations on integer solutions of Pell and Diophantine equations, finite continued fractions and fundamental solutions, Pell and Diophantine equation over finite fields. |
8 |
NUMBERS |
Kaprekar numbers, Fibonacci, Lucas, Pell and Carmichael numbers. |
9 |
CONGRUENCES |
Quadratic and cubic congruence and their connections with binary quadratic forms, integer solutions of cubic and quadratic congruences over finite fields. |
10 |
CONICS |
Conics over finite fields and the number of rational points on conics related to binary quadratic forms over finite fields. |
7) PUBLICATIONS: (Indexed by MathSci Net) (Indexed by Zentralblatt MATH )
- A.Tekcan , M.Bayraktar, O.Bizim. On the Covering Space and the Automorphism Group of the Covering Space. Balkan J. of Geo. and Its Apl. 8(1) (2003), 101-108. (SCI-Exp)
- A.Tekcan , O.Bizim. The Connection between Quadratic Forms and the Extended Modular Group. Mathematica Bohemica128(3) (2003), 225-236.
- A .Tekcan , O.Bizim. On the Number of Representations of Positive Integers by Quadratic Forms as the Basis of the Space $S_{4}(\Gamma_{0}(47),1) $ . Int. Jour. of Maths. and Math. Sci.2004(12) (2004), 637-646.
- A.Te kcan, O.Bizim. On the Representation of Positive Integers by Quadratic Forms with Seven Variables . South East Asian Bull. of Mathematics28 (5) (2004), 875-886.
- A.Te kcan.Representations of Positive Integers by a Direct Sum of Quadratic Forms .Results in Maths.46(2004), 146-163.(SCI-Exp)
- A.T ekcan. Pell Equation $x^{2}-Dy^{2}=2$, II.Irish Mathematical Society Bulletin54(2004), 73-89.
- A .Tekcan.Formulas for the Fourier Coefficients of Cusp Form for Some Quadratic Forms. Turkish Journal of Mathematics29(2005), 141-156. (SCI-Exp)
- A .Tekcan. Representation of Integers by Hermitian Forms . Acta Mathematica Universitatis ComenianaeLXXIV(2) (2005), 205-209.
- A .Tekcan.Cycles of Indefinite Quadratic Forms and Cycles of Ideals. Hacettepe Journal of Maths.and Statistics35(1) (2006), 63-70.
- A .Tekcan, O.Bizim, M.Bayraktar. S olving the Pell Equation using the Fundamental Element of the Field $\mathbb{Q}(\sqrt{\Delta })$ . South East Asian Bull. of Mathematics30(2)(2006), 355-366.
- A .Tekcan.Signatures of the Special Congruence Subgroup of the Extended Modular Group. South East Asian Bulletin of Mathematics30(6) (2006), 1147-1156.
- A .Tekcan, H.Özden. On the Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms. Irish Mathematical Society Bulletin58(2006), 69-79.
- A .Tekcan, O.Bizim, I.N.Cangül. The Number of Representations of Positive Integers by Positive Quadratic Forms. Proc. of the Jangjeon Math. Soc. 9 (2) (2006), 125-136.
- A .Tekcan. A Second Approach to the Proper Cycles of Indefinite Quadratic Forms and their Right Neighbors. Int. Journal of Contemporary Math. Sci. 2(6) (2007), 249-260.
- A .Tekcan. The Pell Equation $x^{2}-Dy^{2}=\pm 4$.Applied Mathematical Sciences 1(8)(2007), 363-369.
- A .Tekcan.Representations of Positive Integers by Positive Quadratic Forms and the Fourier Coefficients of Cusp Forms. South East Asian Bull. of Mathematics31(2)(2007), 349-362.
- A .Tekcan.The Number of Rational Points on Conics $C_{p,k}:x^{2}-ky^{2}=1$ over Finite Fields $\mathbb{F}_{p}$. Int. Jour. of Math.Sci.1(2) (2007), 150-153.
- A .Tekcan.The Elliptic Curves $y^{2}=x^{3}-t^{2}x$ over $\mathbb{F}_{p}$.International Journal of Computational and Mathematical Sciences1(3)(2007), 165-171.
- B. Gezer, H.Özden, A.Tekcan, O.Bizim. The Number of Rational Points on Elliptic Curves $y^{2}=x^{3}+b^{2}$ over Finite Fields. International Journal of Computational and Mathematical Sciences1(3) (2007), 178-184
- A.Tekcan. On Indefinite Binary Quadratic Forms, Cubic Congruence and Elliptic Curves . International Journal of Computational and Mathematical Sci. 2(21)(2007), 1031–1037.
- A.Tekcan , B.Gezer, O.Bizim. On the Integer Solutions of the Pell Equation $x^{2}-dy^{2}=2^{t}$. Int. Jour. of Comp. and Math. Sci. 1(3)(2007), 204-208.
- A.Tekcan.Some Algebraic Properties of Universal and Regular Covering Spaces. International Journal of Computational and Mathematical Sciences1(4)(2007), 251-254.
- A .Tekcan.Some Remarks on Indefinite Binary Quadratic Forms and Quadratic Ideals. Hacettepe Journal of Math.and Statistics36(1)(2007), 27-36. (SCI-Exp)
- A.Tekcan.On the Pell Equation $x^{2}-(k^{2}-2)y^{2}=2^{t}$.Crux Mathematicorum with Math. Mayhem 33(6)(2007), 361-365.
- A.Tekcan.Proper Cycle of Indefinite Quadratic Forms and their Right Neighbors. Applications of Mathematics 52 (5) (2007), 407-415.
- A. Tekcan. The Cubic Congruence $x^{3}+ax^{2}+bx+c \equiv 0 (\mod p)$ and Binary Quadratic Forms F(x,y)=ax^{2}+bxy+cy^{2}$ . Ars Combinatoria 85 (2007), 257-269. (SCI-Exp)
- A.Tekcan , B. Gezer, O. Bizim. Some Relations on Lucas Numbers and their Sums . Advanced Studies in Contemporary Mathematics 15(2)(2007), 195-211.
- A.T ekcan. The Base Points of Indefinite Quadratic Forms in the Cycle and Proper Cycle of an Indefinite Quadratic Form.Hacettepe Journal of Mathematics and Statistics36(2)(2007), 101-114. (SCI-Exp)
- A. T ekcan.The Pell Equation $x^{2}-(k^{2}-k)y^{2}=2^{t}$. Int. Journal of Comp.and Math.Sci.2(1)(2008), 5-9.
- B.Gezer, A.Tekcan, O.Bizim. The Number of Rational Points on Elliptic Curves and Circles over Finite Fields. Int. Journal of Comp.and Math.Sci. 2 (2)(2008), 58-63.
- A.Tekcan.On Indefinite Binary Quadratic Forms and Quadratic Ideals. Novi Sad Journal of Mathematics38(1)(2008), 83-96.
- A. Tekcan , A.Özkoç, B.Gezer, O.Bizim. Some Relations Involving the Sums of Fibonacci Numbers . Proceedings of the Jangjeon Math. Soc. 11(1) (2008), 1-12.
- A.Tekcan , O.Bizim. The Pell Equation $x^{2}+xy-ky^{2}=\pm1$. Global Journal of Pure and Applied Mathematics 4 (2)(2008), 105-112.
- A .Tekcan. On the Cycles of Indefinite Quadratic Forms and Cycles of Ideals III. Comptes rendus mathématiques-Mathematical Reports30(1)(2008), 22-32.
- A. Tekcan , A.Özkoç, B.Gezer, O.Bizim. Elliptic Curves, Conics and Cubic Congruencies associated with Indefinite Binary Quadratic Forms. Novi Sad Journal of Mathematics38(2)(2008), 71-81
- A.Tekcan . The Number of Rational Points on Singular Curves $y^{2}=x(x-a)^{2}$ over Finite Fields $mathbb{F}_{p}$. Int. Journal of Comp.and Math.Sci.3(1)(2009), 14-17.
- A. Tekcan , A.Özkoç. Quadratic Irrationals, Quadratic Ideals and Indefinite Quadratic Forms II . Int. Journal of Comp.and Math.Sci.3(2)(2009), 56-59.
- A. Tekcan . Representation of Integers by Quadratic Forms in Several Variables. Creative Mathematics and Informatics 18 (2009), 65-75.
- A.Tekcan , A.Özkoç. Positive Definite Binary Quadratic Forms, Quadratic Congruences and Singular Curves . Comptes ren.math.-Math.Reports31(2)(2009), 53-64
- A.Tekcan.The Elliptic Curves $y^{2}=x^{3}-1728x$ over Finite Fields. Journal of Algebra, Number Theory: Advances and Applications1(1)(2009), 61-74.
- A.Tekcan , A.Ozkoç, H.Alkan. The Diophantine Equation $y^{2}-2yx-3=0$ and Corresponding Curves over $mathbb{F}_{p}$ . International Jour. of Math.and Statis. Sci. 1(2)(2009), 66-69.
- B.Gezer, A. Tekcan , O.Bizim. Elliptic Divisibility Sequences over Finite Fields.Int. Journal of Comp.and Math.Sci. 4(1)(2010), 12-19
- A.Tekcan , A.Özkoç. The Diophantine Equation $x^{2}-(t^{2}+t)y^{2}-(4t+2)x+(4t^{2}+4t)y=0$ . Revista Matemática Complutense23(1)(2010), 251-260 (SCI-Exp)
- A.Tekcan , A.Özkoç, C.Kocapınar, H.Alkan. The Diophantine Equation $x^{2}-Py^{2}=Q . Int. Journal of Comp.and Math.Sci. 4 (2)(2010), 59-62.
- A.Tekcan. On the Cycles of Indefinite Quadratic Forms and Cycles of Ideals II . South East Asian Bulletin of Mathematics34(2010), 185-192.
- A.Tekcan , A.Ozkoç. The Family of Indefinite Binary Quadratic Forms and elliptic Curves over Finite Fields. General Mathematics.
- A.Tekcan.The Elliptic Curves $y^{2}=x(x-1)(x-\lambda)$. Ars Combinatoria (SCI-Exp)
- A .Tekcan.The Number of Solutions of Pell Equations $x^{2}-ky^{2}=N$ and $x^{2}+xy-ky^{2}=N$ over $\mathbb{F}_{p}$. Ars Combinatoria. (SCI-Exp)
- A .Tekcan.Positive Definite Binary Quadratic Forms and Modules over a Field. South East Asian Bulletin of Mathematics
- A.Tekcan , O.Bizim. Elliptic Curves and Cubic Congruences Associated with Indefinite Binary Quadratic Forms. Global Journal of Pure and Applied Mathematics.
- A.Tekcan , A.Özkoç, B.Gezer, O.Bizim. Representations of Positive Integers by Positive Quadratic Forms . South East Asian Bulletin of Mathematics
- A. Tekcan.Some Algebraic Identities on Pell Numbers and Sums of Pell Numbers Ars Combinatoria (SCI-Exp)
- A.Özkoç, A.Tekcan. Quadratic Diophantine Equation $x^{2}-(t^{2}-t)y^{2}-(4t-2)x+(4t^{2}-4t)y=0$ . Bulletin of the Malaysian Mathematical Science Society . (SCI-Exp)
- A .Tekcan.Principal Indefinite Quadratic Forms and Singular Curves over Finite Fields. South East Asian Bulletin of Mathematics .
- A. Tekcan. The Cubic Congruence $x^{3}+ax^{2}+bx+c \equiv 0 (\mod p)$ and Binary Quadratic Forms F(x,y)=ax^{2}+bxy+cy^{2}$ II. Acta Universitatis Apulensis
- A.Tekcan , A.Özkoç . $n$-Universal Quadratic Forms and Quadratic Forms over Finite Fields. Irish Math. Soc.Bulletin .
- A.Tekcan , A.Özkoç, H.Alkan. On Cycles and Products of Ideals and Corresponding Indefinite Quadratic Forms. Comptes ren.math.-Math.Reports
- C.Kocapınar, A.Özkoç, A.Tekcan. T he Integer Sequence $B=B_{n}(P,Q)$ with Parameters $P$ and $Q$ . Ars Combinatoria (SCI-Exp)
- A.Tekcan . On Kaprekar Numbers . Advances in Theoretical and Applied Mathematics.
8) SYMPOSIUM ATTENDED:
A) National:
- A.Tekcan.Quadratic Forms and Ideals. XVII. National Mathematics Symposium, Abant İzzet Baysal University, 2004, Bolu-TURKIYE.
- A .Tekcan. Base Points of Positive Definite Quadratic Forms. XVIII National Mathematics Symposium, İstanbul Kültür University, 2005, İstanbul- TURKIYE.
- A .Tekcan, O.Bizim, H.Özden, İ.İnam. Cycles of Indefinite Quadratic Forms. XIX. National Mathematics Symposium, Dumlupınar University , 2006, Kütahya- TURKIYE.
- H.Özden, İ.İnam, A.Tekcan, O.Bizim. The Number of Rational Points on Elliptic Curves $y^{2}=x^{3}+b^{2}$ over Finite Fields. XIX. National Mathematics Symposium, Dumlupınar University, 2006, Kütahya-TURKIYE.
- İ.İnam, O.Bizim, A.Tekcan, H.Özden. The Rational Points on Frey Elliptic Curves over Finite Fields. XIX. National Mathematics Symposium, Dumlupınar University, 2006, Kütahya-TURKIYE.
- A .Tekcan, A.Özkoç. Right and Left Neighbors of Indefinite Binary Quadratic Forms. XXII. National Mathematics Symposium, Nesin Mathematics Willage , 2009, Selçuk-İzmir, TURKIYE.
- A.Özkoç, A.Tekcan, Indefinite Binary Quadratic Forms, Elliptic Curves and Cubic Congruences. XXII. National Mathematics Symposium, Nesin Mathematics Willage , 2009, Selçuk-İzmir, TURKIYE.
B) International:
- A.Tekcan , B. Gezer , O.Bizim. The Connection between Principal Indefinite Quadratic Forms and Elliptic Curves. Antalya Algebra Days IX, 22-27 May 2007, Antalya-TURKIYE.
- B.Gezer, O. Bizim, A.Tekcan. On the Singular Elliptic Curves over Finite Fields. Antalya Algebra Days IX, 22-27 May 2007, Antalya-TURKIYE.
- A.Tekcan , B. Gezer, O. Bizim. Right Neighbors and Base Points of Indefinite Binary Quadratic Forms. Workshop on Math. Methods in App. Sci., 22-23 May 2008, Bursa-TURKIYE.
- B .Gezer, O. Bizim, A.Tekcan. Some Properties of the Elliptic Divisibility Sequences over Finite Fields . Workshop on Math.Methods in App. Sci., 22-23 May 2008, Bursa-TURKIYE.
- A.Tekcan , A.Özkoç. The Number of Rational Points on Elliptic Curves Related to Binary Quadratic Forms. Antalya Algebra Days X, 28 May- 01 June 2008, Antalya-TURKIYE.
- B.Gezer, A. Özkoç, A.Tekcan, O. Bizim. The Relationship among Elliptic Divisibility Sequences, Elliptic Curves and Binary Quadratic Forms. Antalya Algebra Days X, 28 May- 01 June 2008, Antalya-TURKIYE.
- B.Gezer, O. Bizim, A.Tekcan.On the Elliptic Divisibility Sequences over Finite Fields. 5-th Europan Congress of Mathematics, 14-18 July 2008, Amsterdam-HOLLAND .
9) BOOKS:
1. O.Bizim, A.Tekcan, B.Gezer. General Mathematics I ( ISBN:978-605-4118-18-2) . Dora Publishing, Bursa, 2009.
2. O.Bizim, A.Tekcan, B.Gezer. General Mathematics II ( ISBN:978-605-4118-41-0) . Dora Publishing, Bursa, 2009
10) OTHERS ACADEMIC ACTIVITIONS:
A) Reviewer for
1. Mathematical Reviews MR (2005-)
2. Zentralblatt MATH (2007-)
3. Journal of Number Theory (2008-)
Reviews:
- MR2191752. Dujella Anderj and Petriveviç Vinko . Square roots with many good approximants . Integers 5(3)(2005), A6, 13pp.
- MR2245690. Ramharter Gerhard. Analysis and geometry of a GCD-algorithm. Rend. del Circolo di Palermo Ser.II. Suppl. 77(2006), 541-552.
- MR2309258. Peters Meinhard. Sums of odd squares . Georgian Math. Journal 13(4)(2006), 779-781.
- MR2330433 . Petersen Sebastian. The rank of hyperelliptic Jacobians in families of quadratic twists. Jour. de Théorie des Nombres de Bord. 18(3)(2006), 653-676
- MR2352828. Schmidt Thomas A. and Sheingorn Mark. Classifying low height geodesics on $\Gamma\sp 3\sbs \scr H$. Int. Jour. of Number T. 3(3)(2007), 421-438.
- MR2352832 .Schmidt Thomas A. and Sheingorn Mark. Low height geodesics on $\Gamma\sp 3\sbs\scr H$ height formulas and examples. Int. Journal of Number Theory 3(3) (2007), 475-501.
- MR2368932 . Csajbók Zoltán. On the mappings of elliptic curves defined over $\Bbb Q$ into $[0,1)\sp 2$.Acta Math. Acad. Paedagog. Nyházi 23 (2)(2007), 115-123.
- MR2425007. Eric, Schmutz. Rational points on the unit sphere . Cent Eur. J. Math. 6 (3) (2008), 482-487.
- MR2430795 Lasserre, Jean B. Representation of nonnegative convex polynomials. Arch. Math. (Basel) 91(2)(2008), 126-130.
- Zbl pre05313027 Jason P. Bell, Stefan Gerhold, Martin Klazar and Florian Luca. Non-holonomicity of sequences defined via elementary functions . Annals of Combinatorics 12(1)(2008), 1-16.
- Zbl pre05305286 Gopalan M.A. and Gnanam A.A notable integer sequence. Math. Sci. Res. J. 12(1)(2008), 7-15.
- Zbl pre05354092 Schweiger, Fritz A note on Lyapunov theory for Brun algorithm. Diophantine Approximation 16(2008), 371-379.
- Zbl pre05310287 Huntley, Jonathan. A strong approximation theorem for automorphic representations.
- Zbl pre05540388 Ishibashi Makoto, Kozaki Masanori. On Fibonacci right-angled triangles . Rep. Fac. Sci. Eng., Saga Univ., Math. 36(1)(2007), 1-8.
- Zbl pre05543168 Koo, Koopa Tak-Lun; Stein, William; Wiese, Gabor. On the generation of the coefficient field of a newform by a single Hecke eigenvalue . J. Théor. Nombres Bordx. 20(2)(2008),373-384.
- Zbl pre05558048 Tao, Liqun. A note on the Pell equation $x^2-Dy^2=\pm 4$. Appl. Math. Sci., Ruse3(3)(2009), 115-118.
- Zbl pre05082227 Stoll, Thomas. On a problem of Erdös and Graham concerning digits. Acta Arith. 125(1)(2006), 89-100.
- Zbl pre05541519 Pumplün, S. Some classes of multiplicative forms of higher degree. Commun. Algebra 37(2)(2009), 609-629.
- Zbl pre05522631 Bremner, Andrew. A problem of Ozanam. Proc. Edinb. Math. Soc., II. Ser. 52(1)(2009), 37-44.
- Zblpre05572518 Cheon, Gi-Sang; Kim, Hana; Shapiro, Louis W. A generalization of Lucas Polynomial sequence. Discrete Appl. Math. 157(5)(2009), 920-927.
B) Member of Editorial Board:
1. International Journal of Computational and Mathematical Sciences (2007-)
2. International Journal of Applied Science, Engineering and Technology (2007-)
3. International Journal of Inequalities and Applications (2007-)
C) Local Organization Committee of:
1. Workshop on Mathematical Methods in Applied Sciences , Ma y 22-23, 2008 , Uludag University, Bursa-TURKIYE.
2. The 20 th International Congress of Jangjeon Mathematical Society, August 21-23, 2008 , Uludag University , Bursa-TURKIYE.
11) TEACHING:
Analysis I, Analysis II, Analysis III, Analysis IV, Functional Analysis, Metric Spaces, Vectorial Analysis, Mathematics I, Mathematics II, General Mathematics I, General Mathematics II, Engineering Mathematics, Advanced Mathematics.
12) LINKS:
1. Mathematics Journals List
2. Mathematics on the web
3. MathSciNet
4. Zentralblatt MATH - ZMATH Online Database
5. History Topics: Alphabetical Index
6. The Electronic Library of Mathematics: Mathematical Journals
7. Mathematical Reviews Electronic Review Submission Home
8. Alphabetical List of Mathematical Societies
9. Mathematical Reviews Database
10. European Mathematical Society
11. 2000 Mathematics Subject Classification
12. Science Citation Index
13. Science Citation Index-Expanded
14. Academic Search Premier
15. Turkish Mathematical Society
16. Turkish Journal of Mathematics
17. Tubitak
18. BCMATH programs for binary quadratic form
19. Finding the reduced binary quadratic form
13) UMAT:
Counselor of Uludag University, Society of Mathematics (UMAT)
Last Updated: January 2010
|
|
Anasayfa
|