Research

Major research field: Analytic Number Theory.

Primary research interests:

• gaps between primes

• level of distributions

• divisor correlations

• applications of étale cohomology

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Publications

Peer-reviewed articles

• “Variance of the \(k\)-fold divisor function in arithmetic progressions for individual modulus”. In: Acta Arith. 212.3 (2024): 195–224 (29 pp.). DOI: 10.4064/aa220517-3-11.

  [Link to published version: https://doi.org/10.4064/aa220517-3-11.]

  [Link to arXiv preprint: https://arxiv.org/abs/2205.02354.]

• “Generalized divisor functions in arithmetic progressions: II”. In: Proc. Edinb. Math. Soc. 67.1 (2024): 28–56 (29 pp.). DOI: 10.1017/S0013091523000664. Open access

  [Link to published version: https://doi.org/10.1017/S0013091523000664.]

  [Link to arXiv preprint: https://arxiv.org/abs/2302.12815.]

• “Generalized divisor functions in arithmetic progressions: I”. In: J. Number Theory 227.1 (2021): 30–93 (64 pp.). ISSN: 0022-314X. DOI: 10.1016/j.jnt.2021.03.021.

  [Link to published version: https://doi.org/10.1016/j.jnt.2021.03.021.]

  [Link to arXiv preprint: https://arxiv.org/abs/2308.06839.]

• (with C. Banderier, C. Krattenthaler, A. Krinik, D. Kruchinin, V. Kruchinin, and M. Wallner) “Explicit Formulas for Enumeration of Lattice Paths: Basketball and the Kernel Method”. In: Lattice path combinatorics and applications. Based on the 8th international conference on lattice path combinatorics and applications, California State Polytechnic University, Pomona (Cal Poly Pomona), CA, USA, August 17–20, 2015. Cham: Springer Dev. Math. 58. (2019): 78–118 (41 pp.). ISBN: 978-3-030-11101-4; 978-3-030-11102-1. DOI: 10.1007/978-3-030-11102-1_6.

  [Link to published version: https://doi.org/10.1007/978-3-030-11102-1_6.]

  [Link to arXiv preprint: https://arxiv.org/abs/1609.06473.]

Thesis

• Topics in Multiplicative Number Theory. Thesis (Ph.D.)–University of California, Santa Barbara. ProQuest LLC, Ann Arbor, MI, June 2021, 187 pp. ISBN: 979-8544-27846-7.

  [Link to published version: https://www.proquest.com/docview/2572561145.]

Preprints

• “On Ramanujan–Fourier expansions”. arXiv:2305.17597 [math.NT] (2023), 6 pp.

• “A note on \( \theta_2 \)”. arXiv:2303.08093 [math.NT] (2023), 24 pp.

• “On correlation of the 3-fold divisor function with itself”. arXiv:2206.05877 [math.NT] (2022), 46 pp.

In Preparation

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Talks

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Reviews

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Translations