Scott David Ahlgren

If you made any changes in Pure these will be visible here soon.

Research Output

2019

Dissections of Strange q-Series

Ahlgren, S., Kim, B. & Lovejoy, J., Nov 1 2019, In : Annals of Combinatorics. 23, 3-4, p. 427-442 16 p.

Research output: Contribution to journalArticle

Maass forms and the mock theta function f(q)

Ahlgren, S. & Dunn, A., Aug 6 2019, In : Mathematische Annalen. 374, 3-4, p. 1681-1718 38 p.

Research output: Contribution to journalArticle

2018

A polyharmonic Maass form of depth 3/2 for SL2(Z)

Ahlgren, S., Andersen, N. & Samart, D., Dec 15 2018, In : Journal of Mathematical Analysis and Applications. 468, 2, p. 1018-1042 25 p.

Research output: Contribution to journalArticle

Congruences for a mock modular form on SL2(Z) and the smallest parts function

Ahlgren, S. & Kim, B., Aug 2018, In : Journal of Number Theory. 189, p. 81-89 9 p.

Research output: Contribution to journalArticle

Kloosterman sums and Maass cusp forms of half integral weight for the modular group

Ahlgren, S. & Andersen, N., 2018, In : International Mathematics Research Notices. 2, p. 492-570 79 p.

Research output: Contribution to journalArticle

2016

Algebraic and transcendental formulas for the smallest parts function

Ahlgren, S. & Andersen, N., Feb 5 2016, In : Advances in Mathematics. 289, p. 411-437 27 p.

Research output: Contribution to journalArticle

A note on cusp forms as p-adic limits

Ahlgren, S. & Samart, D., Nov 1 2016, In : Journal of Number Theory. 168, p. 360-373 14 p.

Research output: Contribution to journalArticle

2015

Dissections of a «strange» function

Ahlgren, S. & Kim, B., Aug 5 2015, In : International Journal of Number Theory. 11, 5, p. 1557-1562 6 p.

Research output: Contribution to journalArticle

Euler-like recurrences for smallest parts functions

Ahlgren, S. & Andersen, N., Jan 1 2015, In : Ramanujan Journal. 36, 1, p. 237-248 12 p.

Research output: Contribution to journalArticle

Mock theta functions and weakly holomorphic modular forms modulo 2 and 3

Ahlgren, S. & Byungchan, K. I. M., Jan 20 2015, In : Mathematical Proceedings of the Cambridge Philosophical Society. 158, 1, p. 111-129 19 p.

Research output: Contribution to journalArticle

Weak harmonic Maass forms of weight 5/2 and a mock modular form for the partition function

Ahlgren, S. & Andersen, N., Dec 1 2015, In : Research in Number Theory. 1, 1, 10.

Research output: Contribution to journalArticle

2014

Hecke grids and congruences for weakly holomorphic modular forms

Ahlgren, S. & Andersen, N., 2014, Ramanujan 125. Amer. Math. Soc., Providence, RI, Vol. 627. p. 1-16 16 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Mock modular grids and Hecke relations for mock modular forms

Ahlgren, S. & Kim, B., Jul 1 2014, In : Forum Mathematicum. 26, 4, p. 1261-1287 27 p.

Research output: Contribution to journalArticle

2012

Hecke relations for traces of singular moduli

Ahlgren, S. D., Feb 1 2012, In : Bulletin of the London Mathematical Society. 44, 1, p. 99-105 7 p.

Research output: Contribution to journalArticle

2011

Congruences for newforms and the index of the hecke algebra

Ahlgren, S. & Rouse, J., Apr 1 2011, In : Proceedings of the American Mathematical Society. 139, 4, p. 1247-1261 15 p.

Research output: Contribution to journalArticle

ℓ-adic properties of smallest parts functions

Ahlgren, S., Bringmann, K. & Lovejoy, J., Sep 10 2011, In : Advances in Mathematics. 228, 1, p. 629-645 17 p.

Research output: Contribution to journalArticle

2010

Critical L-values of Level p Newforms (mod p)

Ahlgren, S. & Rouse, J., May 10 2010, In : International Mathematics Research Notices. 2010, 9, p. 1575-1606 32 p.

Research output: Contribution to journalArticle

2009

Congruences for level four cusp forms

Ahlgren, S., Choi, D. & Rouse, J., Jul 2009, In : Mathematical Research Letters. 16, 4, p. 683-701 19 p.

Research output: Contribution to journalArticle

Vanishing of modular forms at infinity

Ahlgren, S., Masri, N. & Rouse, J., Apr 1 2009, In : Proceedings of the American Mathematical Society. 137, 4, p. 1205-1214 10 p.

Research output: Contribution to journalArticle

2008

Odd coefficients of weakly holomorphic modular forms

Ahlgren, S. D. & Boylan, M., Mar 1 2008, In : Mathematical Research Letters. 15, 2-3, p. 409-418 10 p.

Research output: Contribution to journalArticle

On the irreducibility of Hecke polynomials

Ahlgren, S., Jul 1 2008, In : Mathematics of Computation. 77, 263, p. 1725-1731 7 p.

Research output: Contribution to journalArticle

Rank generating functions as weakly holomorphic modular forms

Ahlgren, S. & Treneer, S., 2008, In : Acta Arithmetica. 133, 3, p. 267-279 13 p.

Research output: Contribution to journalArticle

2007

Central critical values of modular L-functions and coefficients of half-integral weight modular forms modulo ℓ

Ahlgren, S. & Boylan, M., Apr 1 2007, In : American Journal of Mathematics. 129, 2, p. 429-454 26 p.

Research output: Contribution to journalArticle

Congruences for modular forms of weights two and four

Ahlgren, S. & Barcau, M., Oct 1 2007, In : Journal of Number Theory. 126, 2, p. 193-199 7 p.

Research output: Contribution to journalArticle

2005

Arithmetic of singular moduli and class polynomials

Ahlgren, S. & Ono, K., Nov 28 2005, In : Compositio Mathematica. 141, 2, p. 293-312 20 p.

Research output: Contribution to journalArticle

Coefficients of half-integral weight modular forms modulo ℓj

Ahlgren, S. D. & Boylan, M., Jan 2005, In : Mathematische Annalen. 331, 1, p. 219-239 21 p.

Research output: Contribution to journalArticle

2004

The arithmetic of Weierstrass points on modular curves X0 (p)

Ahlgren, S., 2004, Galois theory and modular forms. Kluwer Acad. Publ., Boston, MA, Vol. 11. p. 3-12 10 p. (Dev. Math.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

2003

A congruence for the coefficients in a series for π

Ahlgren, S., Jan 1 2003, In : Acta Arithmetica. 107, 2, p. 157-160 4 p.

Research output: Contribution to journalArticle

Arithmetic properties of the partition function

Ahlgren, S. & Boylan, M., Sep 18 2003, In : Inventiones Mathematicae. 153, 3, p. 487-502 16 p.

Research output: Contribution to journalArticle

Higher weierstrass points on X0(p)

Ahlgren, S. & Papanikolas, M., Apr 1 2003, In : Transactions of the American Mathematical Society. 355, 4, p. 1521-1535 15 p.

Research output: Contribution to journalArticle

The theta-operator and the divisors of modular forms on genus zero subgroups

Ahlgren, S., Sep 1 2003, In : Mathematical Research Letters. 10, 5-6, p. 787-798 12 p.

Research output: Contribution to journalArticle

Weierstrass points on X0(p) and supersingular j-invariants

Ahlgren, S. & Ono, K., Feb 1 2003, In : Mathematische Annalen. 325, 2, p. 355-368 14 p.

Research output: Contribution to journalArticle

2002

Integrals of Eisenstein series and derivatives of L-functions

Ahlgren, S., Berndt, B. C., Yee, A. J. & Zaharescu, A., Jan 1 2002, In : International Mathematics Research Notices. 32, p. 1723-1738 16 p.

Research output: Contribution to journalArticle

Zeta functions of an infinite family of K3 surfaces

Ahlgren, S., Ono, K. & Penniston, D., 2002, In : American Journal of Mathematics. 124, 2, p. 353-368 16 p.

Research output: Contribution to journalArticle

2001

Addition and counting: the arithmetic of partitions

Ahlgren, S. & Ono, K., 2001, In : Notices of the American Mathematical Society. 48, 9, p. 978-984 7 p.

Research output: Contribution to journalArticle

Congruence properties for the partition function

Ahlgren, S. & Ono, K., Nov 6 2001, In : Proceedings of the National Academy of Sciences of the United States of America. 98, 23, p. 12882-12884 3 p.

Research output: Contribution to journalArticle

Congruences and conjectures for the partition function

Ahlgren, S. & Ono, K., 2001, $q$-series with applications to combinatorics, number theory, and physics (Urbana, IL, 2000). Amer. Math. Soc., Providence, RI, Vol. 291. p. 1-10 10 p. (Contemp. Math.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Gaussian hypergeometric series and combinatorial congruences

Ahlgren, S., 2001, Symbolic computation, number theory, special functions, physics and combinatorics (Gainesville, FL, 1999). Kluwer Acad. Publ., Dordrecht, Vol. 4. p. 1-12 12 p. (Dev. Math.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Multiplicative relations in powers of Euler's product

Ahlgren, S., Aug 1 2001, In : Journal of Number Theory. 89, 2, p. 222-233 12 p.

Research output: Contribution to journalArticle

The arithmetic of partitions into distinct parts

Ahlgren, S. & Lovejoy, J., Jan 1 2001, In : Mathematika. 48, 1-2, p. 203-211 9 p.

Research output: Contribution to journalArticle

2000

A Gaussian hypergeometric series evaluation and apéry number congruences

Ahlgren, S. & Ono, K., 2000, In : Journal fur die Reine und Angewandte Mathematik. 518, p. 187-212 26 p.

Research output: Contribution to journalArticle

Distribution of the partition function modulo composite integers M

Ahlgren, S., Dec 2000, In : Mathematische Annalen. 318, 4, p. 795-803 9 p.

Research output: Contribution to journalArticle

Modularity of a certain Calabi-Yau threefold

Ahlgren, S. & Ono, K., 2000, In : Monatshefte fur Mathematik. 129, 3, p. 129-177 49 p.

Research output: Contribution to journalArticle

The sixth, eighth, ninth, and tenth powers of ramanujan's theta function

Ahlgren, S., 2000, In : Proceedings of the American Mathematical Society. 128, 5, p. 1333-1338 6 p.

Research output: Contribution to journalArticle

Open Access
1999

Distribution of parity of the partition function in arithmetic progressions

Ahlgren, S., Jun 1999, In : Indagationes Mathematicae. 10, 2, p. 173-181 9 p.

Research output: Contribution to journalArticle

Equations $F(x,y,=0$

Ahlgren, S., 1999, Topics in number theory (University Park, PA, 1997). Kluwer Acad. Publ., Dordrecht, Vol. 467. p. 85-100 16 p. (Math. Appl.).

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

Non-vanishing of the partition function modulo odd primes l

Ahlgren, S., 1999, In : Mathematika. 46, 1, p. 185-192 8 p.

Research output: Contribution to journalArticle

Topics in number theory : in honor of B. Gordon and S. Chowla

Andrews, G. E., Ahlgren, S. D., Ono, K., Chowla, S. & Gordon, B., 1999, Boston: Kluwer Academic.

Research output: Book/Report/Conference proceedingBook

1998

A binomial coefficient identity associated to a conjecture of Beukers

Ahlgren, S., Ekhad, S. B., Ono, K. & Zeilberger, D., Jan 1 1998, In : Electronic Journal of Combinatorics. 5, 1, p. 11DUMMY

Research output: Contribution to journalArticle

Open Access