Emre Alkan
Research Interests: Analytic Number Theory
Publications:
1. E. Alkan, Variations on Wolstenholme's theorem, Amer. Math.
Monthly 101 (1994), no. 10, 1001--1004.
2. E. Alkan, Nonvanishing of Fourier coefficients of modular
forms, Proc. Amer. Math. Soc. 131 (2003), no. 6, 1673--1680.
3. E. Alkan, On the enumeration of finite abelian and solvable groups,
J. Number Theory 101 (2003), no. 2, 404--423.
4. E. Alkan, A. Zaharescu, Nonvanishing of Fourier coefficients of
newforms in progressions, Acta Arith. 116 (2005), no. 1, 81--98.
5. E. Alkan, On the sizes of gaps in the Fourier expansion of modular
forms, Canad. J. Math. 57 (2005), no. 3, 449--470.
6. E. Alkan, A. Zaharescu, B-free numbers in short arithmetic
progressions, J. Number Theory 113 (2005), no. 2, 226--243.
7. E. Alkan, A. Zaharescu, Nonvanishing of the Ramanujan tau function
in short intervals, Int. J. Number Theory 1 (2005), no. 1, 45--51.
8. E. Alkan, A. Zaharescu, M. Zaki, Arithmetical functions in several
variables, Int. J. Number Theory 1 (2005), no. 3, 383--399.
9. E. Alkan, T. V. Selvakumaran, A. Zaharescu, A uniform distribution
result for a billiard in a unit square, Glasg. Math. J. 47 (2005),
no. 3, 529--547.
10. E. Alkan, G. Harman, A. Zaharescu, Diophantine approximation
with mild divisibility constraints, J. Number Theory 118
(2006), no. 1, 1--14.
11. E. Alkan, A. Zaharescu, M. Zaki, Unitary convolution for
arithmetical functions in several variables, Hiroshima Math. J.
36 (2006), no. 1, 113--124.
12. E. Alkan, F. Stan, A. Zaharescu, Lehmer k-tuples, Proc.
Amer. Math. Soc. 134 (2006), no. 10, 2807--2815.
13. E. Alkan, A. Zaharescu, A Survey on the distribution of
B-free numbers, Turk. J. Math. 30 (2006), no. 3, 293--308.
14. E. Alkan, A. H. Ledoan, M. Vajaitu, A. Zaharescu, Discrepancy
of fractions with divisibility constraints, Monatsh. Math.
149 (2006), no. 3, 179--192.
15. E. Alkan, A. H. Ledoan, M. Vajaitu, A. Zaharescu, Discrepancy
of sets of fractions with congruence constraints, Rev. Roumaine
Math. Pures Appl. 51 (2006), no. 3, 265--276.
16. E. Alkan, J. Sneed, M. Vajaitu, A. Zaharescu, Wolstenholme
matrices, Math. Reports 8(58) (2006), no. 1, 1--8.
17. E. Alkan, A. H. Ledoan, A. Zaharescu, A parity problem on the
free path length of a billiard in the unit square with pockets (Dedicated
to the celebration of the 75th birthday of E. Wirsing), Funct. Approx.
Comm. Math. 35 (2006), no. 1, 19--36.
18. E. Alkan, A. I. Bonciocat, N. C. Bonciocat, A. Zaharescu,
Square-free criteria for polynomials using no derivatives, Proc.
Amer. Math. Soc. 135 (2007), no. 3, 677--687.
19. E. Alkan, M. Xiong, A. Zaharescu, Local spacings along curves,
J. Math. Anal. Appl. 329 (2007), no. 1, 721--735.
20. E. Alkan, Average size of gaps in the Fourier expansion of
modular forms, Int. J. Number Theory 3 (2007), no. 2,
207--215.
21. E. Alkan, A. H. Ledoan, A. Zaharescu, Dirichlet L-functions
and the index of visible points, Illinois J. Math. 51 (2007),
no. 2, 455--477.
22. E. Alkan, M. Xiong, A. Zaharescu, Arithmetic mean of
differences of Dedekind sums, Monatsh. Math. 151 (2007), no.
3, 175--187.
23. E. Alkan, A. Zaharescu, M. Zaki, Multidimensional averages and
Dirichlet convolution, Manuscripta Math. 123 (2007), no. 3,
251--267.
24. E. Alkan, A. Zaharescu, Consecutive large gaps in sequences
defined by multiplicative constraints, Canad. Math. Bull. 51
(2008), no. 2, 172--181.
25. E. Alkan, A. Zaharescu, On the gaps in the Fourier expansion of
cusp forms, Ramanujan J. 16 (2008), no.1, 41--52.
26. E. Alkan, M. Xiong, A. Zaharescu, Quotients of values of the
Dedekind Eta function, Math. Ann. 342 (2008), no. 1, 157--176.
27. E. Alkan, A. H. Ledoan, M. Vajaitu, A. Zaharescu, On the index
of fractions with square-free denominators in arithmetic progressions,
Ramanujan J. 16 (2008), no. 2, 131--161.
28. E. Alkan, M. Xiong, A. Zaharescu, A bias phenomenon on the
behavior of Dedekind sums, Math. Res. Lett. 15 (2008), no. 5,
1039 – 1052.
29. E. Alkan, A. H. Ledoan, A. Zaharescu, Asymptotic behavior of the
Irrational factor, Acta Math. Hungar. 121 (2008), no. 3, 293 – 305.
30. E. Alkan, Davenport constant for finite abelian groups, Indag. Math. 19
(2008), no. 1, 1--21.
31. E. Alkan, K. Ford, A. Zaharescu, Diophantine approximation with arithmetic
functions I, Trans. Amer. Math. Soc. 361 (2009), no. 5, 2263--2275.
32. E. Alkan, K. Ford, A. Zaharescu, Diophantine approximation with arithmetic
functions II, Bull. London Math. Soc. 41 (2009), no. 4, 676--682.
33. E. Alkan, M. Xiong, A. Zaharescu, Pair correlation of torsion points on
elliptic curves, J. Math. Anal. Appl. 356 (2009), no. 2, 752--763.
34. E. Alkan, M. Xiong, A. Zaharescu, Pair correlation of sums of rationals with
bounded height, J. Reine Angew. Math. (Crelle's Journal) 641 (2010), 21--67.
35. E. Alkan, On Dirichlet L-functions with periodic coefficients and
Eisenstein series (Dedicated to my parents), Monatsh. Math. 163 (2011),
no. 3, 249--280.
36. E. Alkan, On the mean square average of special values of L-functions,
J. Number Theory 131 (2011), no. 8, 1470--1485.
37. E. Alkan, Values of Dirichlet L-functions, Gauss sums and trigonometric
sums, Ramanujan J. 26 (2011), no. 3, 375-398.