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Papers

The following is a list of papers which were supported by the FRG Grant or were inspired by the conversations or events that were part of the FRG.

Index

  • \(\spadesuit\): PI or co-PIs of the grant.

  • \(\heartsuit\): Designated as research scientists in the grant.

  • \(\diamondsuit\): Postdocs supported by the grant.

  • \(\clubsuit\): Other participants in the FRG.

Journal Publications

The following publications were directly financially supported by the FRG:

  1. Olga Balkanova(\(\clubsuit\)), John Brian Conrey(\(\spadesuit\)), and Dmitry Frolenkov. An approximation formula for the shifted cubic moment of automorphic L-functions in the weight aspect, Canadian Journal of Mathematics, First View: 1–24, 2023. (journal)

  2. Siegfred Baluyot(\(\diamondsuit\)) and Cruz Castillo. Sign changes of the error term in the Piltz divisor problem, Int. Math. Res. Not. IMRN, (20): 13191–13220, 2024. (journal, arXiv, mathscinet)

  3. Siegfred Baluyot(\(\diamondsuit\)) and Brian Conrey(\(\spadesuit\)). Moments of zeta and correlations of divisor-sums: stratification and Vandermonde integrals, Mathematika, 70(2): Paper No. e12243, 32, 2024. (journal, arXiv, mathscinet)

  4. Siegfred Alan C. Baluyot(\(\diamondsuit\)), Daniel Alan Goldston(\(\clubsuit\)), Ade Irma Suriajaya, and Caroline L. Turnage-Butterbaugh(\(\heartsuit\)). An unconditional Montgomery theorem for pair correlation of zeros of the Riemann zeta-function, Acta Arith., 214: 357–376, 2024. (journal, arXiv, mathscinet)

  5. Estelle Basor and Brian Conrey(\(\spadesuit\)). Factoring determinants and applications to number theory, Random Matrices Theory Appl., 13(2): Paper No. 2450010, 33, 2024. (journal, arXiv, mathscinet)

  6. Jacques Benatar, Alon Nishry, and Brad Rodgers(\(\heartsuit\)). Moments of polynomials with random multiplicative coefficients, Mathematika, 68(1): 191–216, 2022. (journal, arXiv, mathscinet)

  7. Sandro Bettin(\(\clubsuit\)) and John Brian Conrey(\(\spadesuit\)). Averages of long Dirichlet polynomials, Riv. Math. Univ. Parma (N.S.), 12(1): 1–27, 2021. (journal, arXiv, mathscinet)

  8. Sandro Bettin(\(\clubsuit\)) and Alessandro Fazzari(\(\diamondsuit\)). A weighted one-level density of the non-trivial zeros of the Riemann zeta-function, Math. Z., 307(2): Paper No. 32, 23, 2024. (journal, arXiv, mathscinet)

  9. Jonathan W. Bober, Lara Du, Dan Fretwell, Gene S. Kopp, and Trevor D. Wooley(\(\spadesuit\)). On \(2\)-superirreducible polynomials over finite fields, Indag. Math. (N.S.), in press: 1–11, 2024. (journal, arXiv)

  10. Julia Brandes and Trevor D. Wooley(\(\spadesuit\)). Optimal mean value estimates beyond Vinogradov's mean value theorem, Acta Arith., 200(2): 149–182, 2021. (journal, arXiv, mathscinet)

  11. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). An instance where the major and minor arc integrals meet, Bull. Lond. Math. Soc., 51(6): 1113–1128, 2019. (journal, arXiv, mathscinet)

  12. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). A paucity problem for certain triples of diagonal equations, Bull. Lond. Math. Soc., 54(4): 1396–1412, 2022. (journal, arXiv, mathscinet)

  13. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). On smooth Weyl sums over biquadrates and Waring's problem, Acta Arith., 204(1): 19–40, 2022. (journal, arXiv, mathscinet)

  14. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). On Waring's problem for larger powers, J. Reine Angew. Math., 805: 115–142, 2023. (journal, arXiv, mathscinet)

  15. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). Pairs of diagonal quartic forms: the asymptotic formulae, Int. Math. Res. Not. IMRN, (18): 15928–15975, 2023. (journal, arXiv, mathscinet)

  16. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). Pairs of diagonal quartic forms: the non-singular Hasse principle, Q. J. Math., 74(1): 101–128, 2023. (journal, arXiv, mathscinet)

  17. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). Estimates for smooth Weyl sums on major arcs, Int. Math. Res. Not. IMRN, in press: 1–27, 2024. (journal, arXiv)

  18. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). On Waring's problem: beyond Freĭman's theorem, J. Lond. Math. Soc. (2), 109(1): Paper No. e12820, 25, 2024. (journal, arXiv, mathscinet)

  19. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). Partitio Numerorum: sums of a prime and a number of \(k\)-th powers, J. Eur. Math. Soc. (JEMS), online first:1–26, 2024. (journal, arXiv)

  20. Jörg Brüdern and Trevor D. Wooley(\(\spadesuit\)). Partitio Numerorum: sums of squares and higher powers, Funct. Approx. Comment. Math., 71(1): 21–67, 2024. (journal, arXiv, mathscinet)

  21. Emanuel Carneiro, Mithun Kumar Das, Alexandra Florea(\(\clubsuit\)), Angel V. Kumchev, Amita Malik(\(\diamondsuit\)), Micah B. Milinovich(\(\clubsuit\)), Caroline Turnage-Butterbaugh(\(\heartsuit\)), and Jiuya Wang. Hilbert transforms and the equidistribution of zeros of polynomials, J. Funct. Anal., 281(9): Paper No. 109199, 25, 2021. (journal, arXiv, mathscinet)

  22. Giacomo Cherubini and Alessandro Fazzari(\(\diamondsuit\)). Hyperbolic Angles from Heegner Points, Michigan Mathematical Journal, Advance Publication: 1–28, 2024. (journal, arXiv)

  23. Brian Conrey(\(\spadesuit\)). Character sums and the Riemann Hypothesis, Acta Arith., 214: 327–342, 2024. (journal, arXiv, mathscinet)

  24. Brian Conrey(\(\spadesuit\)) and Alessandro Fazzari(\(\diamondsuit\)). Averages of long Dirichlet polynomials with modular coefficients, Mathematika, 69(4): 1060–1080, 2023. (journal, arXiv, mathscinet)

  25. Alessandro Fazzari(\(\diamondsuit\)). A survey on a weighted one-level density of families of L-functions, Rend. Semin. Mat. Univ. Politec. Torino, 80(1): 29–40, 2022. (journal, mathscinet)

  26. Alessandro Fazzari(\(\diamondsuit\)). A Voronoi summation formula for the shifted triple divisor function, Ramanujan J., 63(4): 1179–1198, 2024. (journal, arXiv, mathscinet)

  27. J. B. Friedlander, D. A. Goldston(\(\clubsuit\)), H. Iwaniec(\(\spadesuit\)), and A. I. Suriajaya. Exceptional zeros and the Goldbach problem, J. Number Theory, 233: 78–86, 2022. (journal, mathscinet)

  28. Daniel A. Goldston(\(\clubsuit\)), Timothy S. Trudgian, and Caroline L. Turnage-Butterbaugh(\(\heartsuit\)). On the Montgomery-Odlyzko method regarding gaps between zeros of the zeta-function, J. Math. Anal. Appl., 527(2): Paper No. 127548, 7, 2023. (journal, arXiv, mathscinet)

  29. Ofir Gorodetsky(\(\clubsuit\)), Alexander Mangerel, and Brad Rodgers(\(\heartsuit\)). Squarefrees are Gaussian in short intervals, J. Reine Angew. Math., 795: 1–44, 2023. (journal, arXiv, mathscinet)

  30. Ofir Gorodetsky(\(\clubsuit\)), Kaisa Matomäki, Maksym Radziwiłł, and Brad Rodgers(\(\heartsuit\)). On the variance of squarefree integers in short intervals and arithmetic progressions, Geom. Funct. Anal., 31(1): 111–149, 2021. (journal, arXiv, mathscinet)

  31. Ofir Gorodetsky(\(\clubsuit\)) and Brad Rodgers(\(\heartsuit\)). The variance of the number of sums of two squares in \(\Bbb F_q[T]\) in short intervals, Amer. J. Math., 143(6): 1703–1745, 2021. (journal, arXiv, mathscinet)

  32. Winston Heap, Anurag Sahay(\(\clubsuit\)), and Trevor D. Wooley(\(\spadesuit\)). A paucity problem associated with a shifted integer analogue of the divisor function, J. Number Theory, 242: 660–668, 2023. (journal, arXiv, mathscinet)

  33. Winston Heap and K. Soundararajan(\(\spadesuit\)). Lower bounds for moments of zeta and L-functions revisited, Mathematika, 68(1): 1–14, 2022. (journal, arXiv, mathscinet)

  34. Henryk Iwaniec(\(\spadesuit\)). The sixth power moment of partial Riemann zeta function and Kloosterman sums, Funct. Approx. Comment. Math., 71(1): 121–125, 2024. (journal, mathscinet)

  35. Vivian Kuperberg(\(\clubsuit\)), Brad Rodgers(\(\heartsuit\)), and Edva Roditty-Gershon. Sums of singular series and primes in short intervals in algebraic number fields, Ramanujan J., 58(2): 291–317, 2022. (journal, arXiv, mathscinet)

  36. Amita Malik(\(\diamondsuit\)) and Neha Prabhu. Equidistribution of \(\alpha p^\theta\) with a Chebotarev condition and applications to extremal primes, Mathematika, 68(3): 595–619, 2022. (journal, arXiv, mathscinet)

  37. D. T. Nguyen(\(\diamondsuit\)). Generalized divisor functions in arithmetic progressions: II, Proc. Edinb. Math. Soc. (2), 67(1): 28–56, 2024. (journal, arXiv, mathscinet)

  38. David T. Nguyen(\(\diamondsuit\)). Variance of the \(k\)-fold divisor function in arithmetic progressions for individual modulus, Acta Arith., 212(3): 195–223, 2024. (journal, arXiv, mathscinet)

  39. Lillian B. Pierce, Caroline L. Turnage-Butterbaugh(\(\heartsuit\)), and Melanie Matchett Wood. On a conjecture for \(\ell\)-torsion in class groups of number fields: from the perspective of moments, Math. Res. Lett., 28(2): 575–621, 2021. (journal, arXiv, mathscinet)

  40. Brad Rodgers(\(\heartsuit\)) and Harshith Sai Vallabhaneni. Autocorrelations of characteristic polynomials for the alternative circular unitary ensemble, Glasg. Math. J., 66(1): 51–64, 2024. (journal, arXiv, mathscinet)

  41. Aleksander Simonić, Timothy S. Trudgian, and Caroline L. Turnage-Butterbaugh(\(\heartsuit\)). Some explicit and unconditional results on gaps between zeroes of the Riemann zeta-function, Trans. Amer. Math. Soc., 375(5): 3239–3265, 2022. (journal, arXiv, mathscinet)

  42. Kannan Soundararajan(\(\spadesuit\)) and Max Wenqiang Xu(\(\clubsuit\)). Central limit theorems for random multiplicative functions, J. Anal. Math., 151(1): 343–374, 2023. (journal, arXiv, mathscinet)

  43. Trevor D. Wooley(\(\spadesuit\)). Finite abelian groups via congruences, Amer. Math. Monthly, 130(5): 482–484, 2023. (journal, arXiv, mathscinet)

  44. Trevor D. Wooley(\(\spadesuit\)). Paucity problems and some relatives of Vinogradov's mean value theorem, Math. Proc. Cambridge Philos. Soc., 175(2): 327–343, 2023. (journal, arXiv, mathscinet)

  45. Trevor D. Wooley(\(\spadesuit\)). The paucity problem for certain symmetric Diophantine equations, Bull. Aust. Math. Soc., 108(1): 29–39, 2023. (journal, arXiv, mathscinet)

  46. Trevor D. Wooley(\(\spadesuit\)). Subconvexity in inhomogeneous Vinogradov systems, Q. J. Math., 74(1): 389–418, 2023. (journal, arXiv, mathscinet)

  47. Trevor D. Wooley(\(\spadesuit\)). Subconvexity in the inhomogeneous cubic Vinogradov system, J. Lond. Math. Soc. (2), 107(2): 798–817, 2023. (journal, arXiv, mathscinet)

  48. Trevor D. Wooley(\(\spadesuit\)). Rational lines on diagonal hypersurfaces and subconvexity via the circle method, Trans. Amer. Math. Soc., 377(3): 2125–2147, 2024. (journal, arXiv, mathscinet)

The following publications were based on, inspired by, or benefitted from seminars, events, and conversations that took place in the ambit of the FRG:

  1. Hung M. Bui(\(\clubsuit\)), Daniel A. Goldston(\(\clubsuit\)), Micah B. Milinovich(\(\clubsuit\)), and Hugh L. Montgomery. Small gaps and small spacings between zeta zeros, Acta Arith., 210: 133–153, 2023. (journal, arXiv, mathscinet)

  2. D. A. Goldston(\(\clubsuit\)) and Ade Irma Suriajaya. The prime number theorem and pair correlation of zeros of the Riemann zeta-function, Res. Number Theory, 8(4): Paper No. 71, 10, 2022. (journal, arXiv, mathscinet)

  3. Daniel A. Goldston(\(\clubsuit\)) and Ade Irma Suriajaya. On a smoothed average of the number of Goldbach representations, In Number theory in memory of Eduard Wirsing, pages 145–156. Springer, Cham, © 2023. (journal, arXiv, mathscinet)

  4. Daniel A. Goldston(\(\clubsuit\)) and Ade Irma Suriajaya. On an average Goldbach representation formula of Fujii, Nagoya Math. J., 250: 511–532, 2023. (journal, arXiv, mathscinet)

  5. Winston Heap and Anurag Sahay(\(\clubsuit\)). The fourth moment of the Hurwitz zeta function, J. Reine Angew. Math., Ahead of Print: 1–29, 2024. (journal, arXiv)

  6. Vivian Kuperberg(\(\clubsuit\)) and Matilde Lalín(\(\clubsuit\)). Sums of divisor functions and von Mangoldt convolutions in \(\Bbb F_q[T]\) leading to symplectic distributions, Forum Math., 34(3): 711–747, 2022. (journal, arXiv, mathscinet)

  7. Chung-Hang Kwan(\(\clubsuit\)). Spectral moment formulae for \(\operatorname{GL}(3) \times \operatorname{GL}(2)\) \(L\)-functions I: The cuspidal case, Algebra Number Theory, 18(10): 1817–1862, 2024. (journal, arXiv, mathscinet)

  8. Chung-Hang Kwan(\(\clubsuit\)). Spectral moment formulae for \(GL(3) \times GL(2)\) \(L\)-functions III: The twisted case, Math. Ann., in press, 2024. (journal, arXiv)

  9. Anurag Sahay(\(\clubsuit\)). Moments of the Hurwitz zeta function on the critical line, Math. Proc. Cambridge Philos. Soc, 174(3): 631-661, 2023. (journal, arXiv, mathscinet)

Preprints

The following preprints were directly supported by the FRG:

  1. Emilia Alvarez(\(\clubsuit\)), Brian Conrey(\(\spadesuit\)), Michael O. Rubinstein(\(\clubsuit\)), and Nina C. Snaith(\(\clubsuit\)). Moments of the derivative of the characteristic polynomial of unitary matrices, 2024, submitted. (arXiv:2407.13124v2)

  2. Theodoros Assiotis, Mustafa Alper Gunes, Jonathan P. Keating(\(\spadesuit\)), and Fei Wei(\(\diamondsuit\)). Exchangeable arrays and integrable systems for characteristic polynomials of random matrices, 2024, submitted. (arXiv:2407.19233v3)

  3. Siegfred Baluyot(\(\diamondsuit\)), Vorrapan Chandee(\(\clubsuit\)), and Xiannan Li(\(\clubsuit\)). Low-lying zeros of a large orthogonal family of automorphic \(L\)-functions, 2024, submitted. (arXiv:2310.07606v3)

  4. Siegfred Baluyot(\(\diamondsuit\)) and Caroline L. Turnage-Butterbaugh(\(\heartsuit\)). Twisted \(2k\)th moments of primitive Dirichlet \(L\)-functions: beyond the diagonal, 2022, submitted. (arXiv:2205.00641v1)

  5. M. Čech(\(\clubsuit\)). Moments of real Dirichlet \(L\)-functions and multiple Dirichlet series, 2024, submitted. (arXiv:2402.07473v2)

  6. J. Champagne, T. H. Lê, Y. R. Liu, and T. D. Wooley(\(\spadesuit\)). Well-distribution modulo one and the primes, 2024, submitted. (arXiv:2406.19491v1)

  7. Brian Conrey(\(\spadesuit\)) and Brad Rodgers(\(\heartsuit\)). Averages of quadratic twists of long Dirichlet polynomials, 2022, submitted. (arXiv:2208.01783v1)

  8. Brian Conrey(\(\spadesuit\)) and Neil Shah. Which numbers are not the sum plus the product of three positive integers?, 2022, submitted. (arXiv:2112.15551v2)

  9. Steven M. Gonek(\(\clubsuit\)) and Anurag Sahay(\(\clubsuit\)). Consecutive moderate gaps between zeros of the Riemann zeta function, 2024, submitted. (arXiv:2412.15481v1)

  10. Alessandro Fazzari(\(\diamondsuit\)). On the joint second moment of zeta and its logarithmic derivative, 2024, accepted, to appear in Acta Arith. (arXiv:2310.15918v2)

  11. Thái Hoàng Lê, Yu-Ru Liu, and Trevor D. Wooley(\(\spadesuit\)). Equidistribution of polynomial sequences in function fields, with applications, 2023, submitted. (arXiv:1311.0892v2)

  12. Amita Malik(\(\diamondsuit\)). Partitions into primes with a Chebotarev condition, 2024, submitted.

  13. A. M. Masullo(\(\diamondsuit\)). Crystalline cohomology over general bases, 2020, submitted. (arXiv:2011.11182v1)

  14. David T. Nguyen(\(\diamondsuit\)). On correlation of the 3-fold divisor function with itself, 2023, submitted. (arXiv:2206.05877v2)

  15. Nick Simm and Fei Wei(\(\diamondsuit\)). On moments of the derivative of CUE characteristic polynomials and the Riemann zeta function, 2024, submitted. (arXiv:2409.03687v1)

  16. Trevor D. Wooley(\(\spadesuit\)). Subconvexity and the Hilbert-Kamke Problem, 2022, submitted. (arXiv:2201.02699v1)

  17. Trevor D. Wooley(\(\spadesuit\)). Condensation and densification for sets of large diameter, 2023, accepted, to appear in Combinatorial and Additive Number Theory VI – CANT, New York, USA, 2022 and 2023, Ed. Melvyn B. Nathanson, Springer Proceedings in Mathematics and Statistics. (arXiv:2305.19968v1)

The following preprints were based on, inspired by, or benefitted from seminars, events, and conversations that took place in the ambit of the FRG:

  1. Yacine Barhoumi-Andréani. A new approach to the characteristic polynomial of a random unitary matrix, 2020, submitted. (arXiv:2011.02465v1)

  2. Vivian Kuperberg(\(\clubsuit\)) and Matilde Lalín(\(\clubsuit\)). Symplectic conjectures for sums of divisor functions and explorations of an orthogonal regime, 2024, accepted, to appear in Trans. Amer. Math. Soc. (arXiv:2212.04969v2)

  3. Chung-Hang Kwan(\(\clubsuit\)). Spectral moment formulae for \(GL(3)\times GL(2)\) \(L\)-functions II: The Eisenstein case, 2023, submitted. (arXiv:2310.09419v1)

  4. Chung-Hang Kwan(\(\clubsuit\)) and Wing Hong Leung. Character sums, reciprocity and functional equations, 2024, submitted. (arxiv:2410.11193v1)

  5. Chung-Hang Kwan(\(\clubsuit\)) and Wing Hong Leung. Trace formula and functional equation, 2024, submitted. (arxiv:2410.16921v1)

  6. Will Sawin(\(\clubsuit\)). A refined random matrix model for function field L-functions, 2024, submitted. (arXiv:2409.02876v1)