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  1. Content type: Research

    In 2013, Lemke Oliver classified all eta-quotients which are theta functions. In this paper, we unify the eta–theta functions by constructing mock modular forms from the eta–theta functions with even character...

    Authors: Amanda Folsom, Sharon Garthwaite, Soon-Yi Kang, Holly Swisher and Stephanie Treneer

    Citation: Research in Number Theory 2016 2:14

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  2. Content type: Research

    Theta representations appear globally as the residues of Eisenstein series on covers of groups; their unramified local constituents may be characterized as subquotients of certain principal series. A cuspidal ...

    Authors: Solomon Friedberg and David Ginzburg

    Citation: Research in Number Theory 2016 2:16

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  3. Content type: Research

    We exploit transformations relating generalized q-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as

    Authors: Robert Schneider

    Citation: Research in Number Theory 2016 2:9

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  4. Content type: Research

    In 1982, Gessel showed that the Apéry numbers associated to the irrationality of ζ(3) satisfy Lucas congruences. Our main result is to prove corresponding congruences for all known sporadic Apéry-like sequences. ...

    Authors: Amita Malik and Armin Straub

    Citation: Research in Number Theory 2016 2:5

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  5. Content type: Research Article

    We discuss the mean values of multiplicative functions over function fields. In particular, we adapt the authors’ new proof of Halász’s theorem on mean values to this simpler setting. Several of the technical ...

    Authors: Andrew Granville, Adam J. Harper and Kannan Soundararajan

    Citation: Research in Number Theory 2015 1:25

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  6. Content type: Research

    We use a generalized Lambert series identity due to the first author to present q-series proofs of recent results of Imamoğlu, Raum and Richter concerning recursive formulas for the coefficients of two 3rd order ...

    Authors: Song Heng Chan, Renrong Mao and Robert Osburn

    Citation: Research in Number Theory 2015 1:29

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  7. Content type: Research

    We revisit Huber’s theory of continuous valuations, which give rise to the adic spectra used in his theory of adic spaces. We instead consider valuations which have been reified, i.e., whose value groups have bee...

    Authors: Kiran S. Kedlaya

    Citation: Research in Number Theory 2015 1:20

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  8. Content type: Research

    We study the leading digit laws for the matrix entries of a linear Lie group G. For non-compact G, these laws generalize the following observations: (1) the normalized Haar measure of the Lie group

    Authors: Corey Manack and Steven J. Miller

    Citation: Research in Number Theory 2015 1:22

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  9. Content type: Research

    Mock modular forms, which give the theoretical framework for Ramanujan’s enigmatic mock theta functions, play many roles in mathematics. We study their role in the context of modular para...

    Authors: Claudia Alfes, Michael Griffin, Ken Ono and Larry Rolen

    Citation: Research in Number Theory 2015 1:24

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  10. Content type: Research Article

    In 1919, P. A. MacMahon studied generating functions for generalized divisor sums. In this paper, we provide a framework in which to view these generating functions in terms of Jacobi forms, and prove that the...

    Authors: Simon CF Rose

    Citation: Research in Number Theory 2015 1:18

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  11. Content type: Research Article

    In a recent paper, Griffin, Ono and Warnaar present a framework for Rogers-Ramanujan type identities using extended Hall-Littlewood polynomials P λ (x ...

    Authors: Hannah Larson

    Citation: Research in Number Theory 2015 1:13

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  12. Content type: Research Article

    Riemann’s non-differentiable function and Gauss’s quadratic reciprocity law have attracted the attention of many researchers. Here we provide a combined proof of both the facts. In (Proc. Int. Conf.–NT 1;107–1...

    Authors: Kalyan Chakraborty, Shigeru Kanemitsu and Li Hai Long

    Citation: Research in Number Theory 2015 1:14

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  13. Content type: Research Article

    Using results from the theory of modular forms, we reprove and extend a result of Romik about lacunary recurrence relations for Eisenstein series.

    Authors: Michael H Mertens and Larry Rolen

    Citation: Research in Number Theory 2015 1:9

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  14. Content type: Research Article

    We establish Sturm bounds for degree g Siegel modular forms modulo a prime p, which are vital for explicit computations. Our inductive proof exploits Fourier-Jacobi expansions of Siegel modular forms and properti...

    Authors: Olav K Richter and Martin Westerholt-Raum

    Citation: Research in Number Theory 2015 1:5

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  15. Content type: Research Article

    We use the theory of congruences between modular forms to prove the existence of newforms with square-free level having a fixed number of prime factors such that the degree of their coefficient fields is arbit...

    Authors: Luis Víctor Dieulefait, Jorge Jiménez Urroz and Kenneth Alan Ribet

    Citation: Research in Number Theory 2015 1:2

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