Scott Ahlgren

Papers

  1. Maass forms and the mock theta function f(q) with A. Dunn
    Math. Annalen (to appear) arxiv
  2. Dissections of strange q-series with B. Kim and J. Lovejoy
    Submitted. arxiv
  3. A polyharmonic Maass form of depth 3/2 for SL2(Z) with N. Andersen and D. Samart
    J. Math. Anal. Appl. Volume 468, Issue 2, December 2018, 1018-1042 journal arxiv
  4. Congruences for a mock modular form on SL2(Z) and the smallest parts function with B. Kim
    J. Number Theory, Volume 189, (2018), 81-89. journal arxiv
  5. Kloosterman sums and Maass cusp forms of half integral weight with N. Andersen
    Int. Math. Res. Notices (2018) Issue 2, 492-570. journal arxiv
  6. A note on cusp forms as p-adic limits with D. Samart
    J. Number Theory 168 (2016), 360-373. journalarxiv
  7. Algebraic and transcendental formulas for the smallest parts function with N. Andersen
    Adv. Math. 289 (2016), 411--437. journalarxiv
  8. Dissections of a "strange" function with B. Kim
    Int. J. Number Theory 11 (2015), no. 5, 1557–1562. journal arxiv
  9. Euler-like recurrences for smallest parts functions with N. Andersen
    Ramanujan J. (special issue in honor of Basil Gordon) 36 (2015), no. 1-2, 237–248. journal arxiv
  10. Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function with N. Andersen
    Res. Num. Theory (2015) 1:10, 1-16. journal arxiv
  11. Mock theta functions and weakly holomorphic modular forms modulo 2 and 3 with B. Kim
    Math. Proc. Cambridge Philos. Soc. 158 (2015), no. 1, 111–129. journal arxiv
  12. Hecke grids and congruences for weakly holomorphic modular forms with N. Andersen
    Ramanujan 125, 1–16, Contemp. Math., 627, Amer. Math. Soc. (2014). journal arxiv
  13. Mock modular grids and Hecke relations for mock modular forms with B. Kim
    Forum Math. 26 (2014), no. 4, 1261–1287. journal
  14. Hecke relations for traces of singular moduli
    Bull. Lond. Math. Soc. 44 (2012), no. 1, 99–105. journal
  15. ℓ-adic properties of smallest parts functions with K. Bringmann and J. Lovejoy
    Adv. Math. 228 (2011), no. 1, 629–645. journal arxiv
  16. Congruences for newforms and the index of the Hecke algebra with J. Rouse
    Proc. Amer. Math. Soc. 139 (2011), no. 4, 1247–1261. journal
  17. Critical L-values of level p newforms (mod p) with J. Rouse
    Int. Math. Res. Not. (2010), no. 9, 1575–1606 journal
  18. Congruences for level four cusp forms with D. Choi and J. Rouse
    Math. Res. Lett. 16 (2009), no. 4, 683–701. journal
  19. Vanishing of modular forms at infinity with N. Masri and J. Rouse
    Proc. Amer. Math. Soc. 137 (2009), no. 4, 1205–1214. journal
  20. Rank generating functions as weakly holomorphic modular forms with S. Treneer
    Acta Arith. 133 (2008), no. 3, 267–279. journal
  21. Odd coefficients of weakly holomorphic modular forms with M. Boylan
    Math. Res. Lett. 15 (2008), no. 3, 409–418. journal
  22. On the irreducibility of Hecke polynomials
    Math. Comp. 77 (2008), no. 263, 1725–1731. journal
  23. Congruences for modular forms of weights two and four with M. Barcau
    J. Number Theory 126 (2007), no. 2, 193–199. journal
  24. Central critical values of modular L-functions and coefficients of half-integral weight modular forms modulo ℓ with M. Boylan
    Amer. J. Math. 129 (2007), no. 2, 429–454. journal
  25. Arithmetic of singular moduli and class polynomials with K. Ono
    Compos. Math. 141 (2005), no. 2, 293–312. journal
  26. Coefficients of half-integral weight modular forms modulo ℓj with M. Boylan
    Math. Ann. 331 (2005), no. 1, 219–239. journal
  27. The arithmetic of Weierstrass points on modular curves X0(p)
    Galois theory and modular forms, 3–12, Dev. Math., 11, Kluwer Acad. Publ., Boston, MA, 2004. journal
  28. The theta-operator and the divisors of modular forms on genus zero subgroups
    Math. Res. Lett. 10 (2003), no. 5-6, 787–798. journal
  29. Arithmetic properties of the partition function with M. Boylan
    Invent. Math. 153 (2003), no. 3, 487–502. journal
  30. A congruence for the coefficients in a series for π
    Acta Arith. 107 (2003), no. 2, 157–160. journal
  31. Weierstrass points on X0(p) and supersingular j-invariants with K. Ono
    Math. Ann. 325 (2003), no. 2, 355–368. journal
  32. Higher Weierstrass points on X0(p) with M. Papanikolas
    Trans. Amer. Math. Soc. 355 (2003), no. 4, 1521–1535 (electronic). journal
  33. Integrals of Eisenstein series and derivatives of L-functions with B. Berndt, A. Yee, and A. Zaharescu
    Int. Math. Res. Not. 2002, no. 32, 1723–1738. journal
  34. Zeta functions of an infinite family of K3 surfaces with K. Ono and D. Penniston
    Amer. J. Math. 124 (2002), no. 2, 353–368. journal
  35. The points of a certain fivefold over finite fields and the twelfth power of the eta function
    Finite Fields Appl. 8 (2002), no. 1, 18–33. journal
  36. The arithmetic of partitions into distinct parts with J. Lovejoy
    Mathematika 48 (2001), no. 1-2, 203–211 (2003). journal
  37. Gaussian hypergeometric series and combinatorial congruences
    Symbolic computation, number theory, special functions, physics and combinatorics (Gainesville, FL, 1999), 1–12, Dev. Math., 4, Kluwer Acad. Publ., Dordrecht, 2001. journal
  38. Congruences and conjectures for the partition function with K. Ono
    q-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000), 1–10, Contemp. Math., 291, Amer. Math. Soc., Providence, RI, 2001. journal
  39. Congruence properties for the partition function with K. Ono
    Proc. Natl. Acad. Sci. USA 98 (2001), no. 23, 12882–12884 (electronic). journal
  40. Addition and counting: the arithmetic of partitions with K. Ono
    Notices Amer. Math. Soc. 48 (2001), no. 9, 978–984.
  41. Multiplicative relations in powers of Euler's product
    J. Number Theory 89 (2001), no. 2, 222–233. journal
  42. Distribution of the partition function modulo composite integers M
    Math. Ann. 318 (2000), no. 4, 795–803. journal
  43. Modularity of a certain Calabi-Yau threefold with K. Ono
    Monatsh. Math. 129 (2000), no. 3, 177–190. journal
  44. A Gaussian hypergeometric series evaluation and Apéry number congruences with K. Ono
    J. Reine Angew. Math. 518 (2000), 187–212. journal
  45. The sixth, eighth, ninth, and tenth powers of Ramanujan's theta function
    Proc. Amer. Math. Soc. 128 (2000), no. 5, 1333–1338. journal
  46. Distribution of parity of the partition function in arithmetic progressions
    Indag. Math. (N.S.) 10 (1999), no. 2, 173–181. journal
  47. Non-vanishing of the partition function modulo odd primes ℓ
    Mathematika 46 (1999), no. 1, 185–192. journal
  48. Equations F(x,y,αx) = 0
    Topics in number theory (University Park, PA, 1997), 85–100, Math. Appl., 467, Kluwer Acad. Publ., Dordrecht, 1999.
  49. The set of solutions of a polynomial-exponential equation
    Acta Arith. 87 (1999), no. 3, 189–207.
  50. A binomial coefficient identity associated to a conjecture of Beukers with S. Ekhad, K. Ono, and D. Zeilberger
    Electron. J. Combin. 5 (1998), Research Paper 10, 1 p. (electronic). journal arxiv
  51. An amusing representation of x/sin x with L. English and R. Winters
    Amer. Math. Monthly 104 (1997), no. 10, 964–966. journal
  52. Polynomial-exponential equations in two variables
    J. Number Theory 62 (1997), no. 2, 428–438. journal

Video

My talk "Algebraic and transcendental formulas for the smallest parts function" at CIRM:


Graduate Students (PhD Year)