Publications and Notes
Publications and Preprints
26. (with Y. You) Large sums of high order characters II (submitted)
25. On a Goldbach-type problem for the Liouville function (IMRN, to appear, DOI: 10.1093/imrn/rnae149)
24. Gap problems for integer-valued multiplicative functions (submitted)
23. On equal consecutive values of multiplicative (submitted)
22. (with O. Klurman and J. Teräväinen) On Elliott's conjecture and applications (submitted)
21. Large sums of high order characters
Journal of the London Mathematical Society, 109(1) (2024), DOI: 10.1112/jlms.12841.
20. Sign changes of fourier coefficients of cusp forms at norm form arguments
Mathematical Proceedings of the Cambridge Philosophical Society 175 (2023), pp. 539--567, https://doi.org/10.1017/S0305004123000294
19. (with O. Klurman and J. Teräväinen) Beyond the Erdos discrepancy problem in function fields
Mathematische Annalen (2023). https://doi.org/10.1007/s00208-023-02700-z
18. (with A. Granville) Three conjectures about character sums
Mathematische Zeitschrift, 305:49 (2023), https://doi.org/10.1007/s00209-023-03374-8
17. (with O. Gorodetsky and B. Rodgers) Squarefrees are Gaussian in short intervals
Journal für die reine und angewandte Mathematik (Crelle's journal) 795 (2023), pp. 1--44, https://doi.org/10.1515/crelle-2022-0066
16. Additive functions in short intervals, gaps and a conjecture of Erdos
The Ramanujan Journal, 59 (2022), pp. 1023–1090, https://doi.org/10.1007/s11139-022-00623-y
15. Divisor-bounded multiplicative functions in short intervals
Research in the Mathematical Sciences 10(12) (2023), 47 pp., https://doi.org/10.1007/s40687-023-00376-0
14. (with O. Klurman and J. Teräväinen) Correlations of multiplicative functions in function fields
Mathematika 69(1) (2023), pp. 155--231, https://doi.org/10.1112/mtk.12181
13. (with O. Klurman) Monotone chains of fourier coefficients of Hecke cusp forms (submitted)
12. Squarefree integers in arithmetic progressions to smooth moduli
Forum of Mathematics, Sigma, 9 (2021), e72, https://doi.org/10.1017/fms.2021.67
11. (with O. Klurman, C. Pohoata and J. Teräväinen) Multiplicative functions that are close to their mean.
Transactions of the American Mathematical Society, 374 (2021), pp. 7967-7990, https://doi.org/10.1090/tran/8427
10. (with O. Klurman and J. Teräväinen) Multiplicative functions in short arithmetic progressions
Proceedings of the London Mathematical Society 127(3) (2023), pp. 366–446, https://doi.org/10.1112/plms.12546
9. Short character sums and the Polya-Vinogradov inequality
Quarterly Journal of Math. 71(4) (2020), pp. 1281-1308, https://doi.org/10.1093/qmath/haaa031
8. (with O. Klurman) On the orbits of multiplicative pairs.
Algebra and Number Theory 14(1) (2020) pp. 155–189, https://doi.org/10.2140/ant.2020.14.155
7. (with O. Klurman) Rigidity theorems for multiplicative functions
Mathematische Annalen 372(1) (2018) pp. 651-697, https://doi.org/10.1007/s00208-018-1724-6
6. (with Y. Lamzouri) Large odd order character sums and improvements of the Polya-Vinogradov inequality
Transactions of the American Mathematical Society 375(6) (2022), pp. 3759--3793. https://doi.org/10.1090/tran/8607
5. On the bivariate Erdos-Kac Theorem and binary correlations of the Mobius function.
Mathematical Proceedings of the Cambridge Philosophical Society (2019) p. 1-59, https://doi.org/10.1017/S0305004119000288
4. Generalizations on a problem of Saffari.
INTEGERS 15 (2015) Paper No. A53, 6 pp.
3. (with O. Klurman) Multilinear averages and sign patterns of multiplicative functions (submitted)
2. On the distribution of integers with restricted prime factors II (superseded by this paper; cleaner result reproduced in my thesis)
1. A strengthening of theorems of Halasz and Wirsing (superseded by this paper; cleaner result reproduced in my thesis)
Unpublished Notes:
4. On the distribution of integers with restricted prime factors I (not intended for publication)
3. On Exponential Sums with the Mobius Function and the Quasi-Riemann Hypothesis
2. The Multiplication Table Problem and its Generalizations (MSc. Thesis)
1. A Short Note on an Argument of Erdos and Mahler.
Lecture Notes:
1. Lecture Notes for a Reading Course in Elliptic Curves, supervised by Dr. M. Rubinstein.
2. Lecture Notes for a Course in Modular Forms by Dr. C. Stewart.
3. Introduction to Analysis (not entirely complete)
Expository Articles:
1. Normal Numbers and Applications of Continued Fractions.
2. Rademacher's Formula for the Partition Function p(n).
3. Expository Note on the Littlewood-Offord Problem in Additive Combinatorics
4. Additive Number Theory and the Representation of Integers (prepared for a talk at the 2014 Canada Math Camp).
5. Introduction to Diophantine Approximation (presented to the Humberside C.I. math club)
Undergraduate Research:
1. "Understanding Ga1-xMnxAs for Use in Spintronics Applications". PHYS13news Number 135 (Undergraduate Physics Journal), University of Waterloo, May 2010.