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Publications, preprints for Cormac O'Sullivan

 

Preprints or recent publications:

 A direct counting approach to the Hurwitz enumeration problem,
    with N. Apostolakis, in preparation.
  

 Topographs for binary quadratic forms and class numbers, arXiv, also video of a talk on this
 

 [2024] Integrality of the higher Rademacher symbols,
    Adv. Math. 455 (2024), Paper No. 109876, 22 pp. arXiv
    

 [2023] Detailed asymptotic expansions for partitions into powers,
    Int. J. Number Theory 19 (2023), no. 9, 2163–2196. arXiv 
  

 [2023] Symmetric functions and a natural framework for combinatorial and number theoretic sequences,
    Res. Number Theory 9 (2023), no. 3, Paper No. 56, 40 pp. arXiv 
  

 [2023] Stirling's approximation and a hidden link between two of Ramanujan's approximations,
    J. Combin. Theory Ser. A 197 (2023), Paper No. 105740, 33 pp. arXiv
     

 [2023] Ramanujan's approximation to the exponential function and generalizations,
    Ramanujan J. 62 (2023), no. 3, 649–673. arXiv  
  

 [2023] A generalization of the Riemann-Siegel formula,
    Math. Z. 303 (2023), no. 1, Paper No. 20, 44 pp. arXiv
  

 [2022] De Moivre and Bell polynomials,
    Expo. Math. 40 (2022), no. 4, 870–893. arXiv
     

 [2022] Limits of Jensen polynomials for partitions and other sequences,
    Monatsh. Math. 199 (2022), no. 1, 203–230. arXiv
       

 [2021] Zeros of Jensen polynomials and asymptotics for the Riemann xi function,
    Res. Math. Sci. 8 (2021), no. 3, Paper No. 46, 27 pp. arXiv
  

 [2020] Transformation laws for generalized Dedekind sums associated to Fuchsian groups,
    with C. Burrin, J. Jorgenson and L. Smajlovic,
    Acta Arith. 196 (2020), no. 2, 139–162. arXiv
  

 [2020] Rademacher's conjecture and expansions at roots of unity of products generating restricted partitions,
    J. Number Theory 216 (2020), 335–379. arXiv
   

 [2020] Modular Dedekind symbols associated to Fuchsian groups and higher-order Eisenstein series,
    with J. Jorgenson and L. Smajlovic, 
    Res. Number Theory 6 (2020), no. 2, Paper No. 22, 42 pp. arXiv
 

 [2019] Noncommutative modular symbols and Eisenstein series,
    with G. Chinta and I. Horozov, Automorphic forms and related topics, 27–45,
    Contemp. Math. 732 Amer. Math. Soc., Providence, RI, 2019.  arXiv
 

 [2019] Revisiting the saddle-point method of Perron,
    Pacific J. Math. 298 (2019), no. 1, 157-199. arXiv
 

 [2018] Partitions and Sylvester waves,
    Ramanujan J. 47 (2018), no. 2, 339–381.  arXiv
 

 [2018] A vertex and edge deletion game on graphs,
    Integers 18 (2018), Paper No. G03, 38 pp. arXiv
  

 [2018] Formulas for non-holomorphic Eisenstein series and for the Riemann zeta function at odd integers,
    Res. Number Theory 4 (2018), no. 3, Art. 36, 38 pp. arXiv
 

 [2016] Hyperbolic Fourier coefficients of Poincare series,
    with K. Taylor. Ramanujan J. 41 (2016), no. 1, 465 - 518.  arXiv
 

 [2016] Asymptotics for the partial fractions of the restricted partition generating function II,
    Integers 16 (2016), Paper No. A78, 73 pp. arXiv
 

 [2016] Zeros of the dilogarithm,
    Math. Comp. 85 (2016), no. 302, 2967-2993. arXiv
 

 [2016] Asymptotics for the partial fractions of the restricted partition generating function, I,
    Int. J. Number Theory 12 (2016), no. 6, 1421-1474. arXiv
 

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Older publications:

 [2015] On the partial fraction decomposition of the restricted partition generating function,
    Forum Math 27 (2015), no. 2, 735 - 766. arXiv
  

 [2013] Kernels for products of L-functions,
    with N. Diamantis. Algebra and Number Theory 7 (2013), no. 8, 1883 - 1917. arXiv
  

 [2013] Nonvanishing of Taylor coefficients and Poincare series,
    with M. Risager. Ramanujan J. 30 (2013), no. 1, 67 - 100. arXiv
 

 [2011] A Diophantine Frobenius problem related to Riemann surfaces,
    with T. Weaver. Glasgow Math. J. 53 (2011), 501 - 522. arXiv
  

 [2010] Kernels of L-functions of cusp forms,
    with N. Diamantis, Math. Annalen 346, (2010), no. 4, 897 - 929. arXiv
 

 [2009] Parabolic, Hyperbolic and Elliptic Poincare Series,
    with O. Imamoglu, Acta Arithmetica 139, (2009), 199 - 228. arXiv
 

 [2009] On the Linear Independence of Roots,
    with R. Carr, Int. J. Number Theory 5 (2009), no 1, 161 - 171. arXiv
 

 [2008] The dimensions of spaces of second-order automorphic forms and their cohomology,
    with N. Diamantis, Trans. Amer. Math. Soc. 360 (2008), no. 11, 5629 - 5666. arXiv
 

 [2008] Unipotent vector bundles and higher-order non-holomorphic Eisenstein series,
    with J. Jorgenson, Journal de Theorie des Nombres de Bordeaux 20 (2008), 131 - 163. arXiv
 

 [2006] L-functions of second-order cusp forms,
    with N. Diamantis, M. Knopp, G. Mason, Ramanujan J. 12 (2006), no. 3, 327 - 347. pdf
 

 [2005] Convolution Dirichlet series and a Kronecker limit formula for second-order Eisenstein series,
    with J. Jorgenson, Nagoya Math. J. 179 (2005), 47-102. arXiv
 

 [2004] Arithmetic progressions with three parts in prescribed ratio and a challenge of Fermat,
    with K. Fogarty, Math. Mag. 77 (2004), no. 4, 282-292. pdf
 

 [2003] Estimating additive character sums for Fuchsian groups,
    with D. Goldfeld, Ramanujan J. 7 (2003), 241-267. pdf
 

 [2002] Second order modular forms,
    with G. Chinta, N. Diamantis, Acta Arith. 103 (2002), 209-223. pdf
 

 [2002] Identities from the holomorphic projection of modular forms,
    Number Theory for the Millennium III, A. K. Peters (2002), 87-106. pdf
 

 [2000] Properties of Eisenstein series formed with modular symbols,
    J. Reine Angew. Math. 518 (2000), 163-186. pdf
 

 [2000] Hecke theory of series formed with modular symbols and relations among convolution L-functions,
    with N. Diamantis, Math. Annalen 318 (1) (2000), 85-105. pdf
  

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