Research
Research in Number Theory 2017 3:21
Published on: 9 October 2017
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Research in Number Theory 2017 3:21
Published on: 9 October 2017
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Research in Number Theory 2017 3:24
Published on: 2 October 2017
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We introduce the notion of primitive elements in arbitrary truncated p-divisible groups. By design, the scheme of primitive elements is finite and locally free over the base. Primitive elements generalize the “po...
Research in Number Theory 2017 3:20
Published on: 8 September 2017
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Research in Number Theory 2017 3:19
Published on: 1 September 2017
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For a given generalized eta-quotient, we show that linear progressions whose residues fulfill certain quadratic equations do not give rise to a linear congruence modulo any prime. This recovers known results f...
Research in Number Theory 2017 3:18
Published on: 9 August 2017
Research
In recent work, Bacher and de la Harpe define and study conjugacy growth series for finitary permutation groups. In two subsequent papers, Cotron, Dicks, and Fleming study the congruence properties of some of ...
Research in Number Theory 2017 3:17
Published on: 1 August 2017
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We study the problem of finding the Artin L-functions with the smallest conductor for a given Galois type. We adapt standard analytic techniques to our novel situation of fixed Galois type and obtain much improve...
Research in Number Theory 2017 3:16
Published on: 10 July 2017
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Research in Number Theory 2017 3:14
Published on: 3 July 2017
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In this paper, we evaluate the Faltings height of an elliptic curve with complex multiplication by an order in an imaginary quadratic field in terms of Euler’s Gamma function at rational arguments.
Research in Number Theory 2017 3:13
Published on: 5 June 2017
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Research in Number Theory 2017 3:11
Published on: 1 June 2017
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We identify a partition-theoretic generalization of Riemann zeta function and the equally positive integer-indexed harmonic sums at infinity, to obtain the generating function and the integral representations ...
Research in Number Theory 2017 3:10
Published on: 10 May 2017
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Research in Number Theory 2017 3:9
Published on: 1 May 2017
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In this paper, we show a non-vanishing result for L-functions associated to cuspidal Hecke eigenforms of half integral weight in plus space.
Research in Number Theory 2017 3:6
Published on: 10 April 2017
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A conjecture connected with quantum physics led N. Katz to discover some amazing mixed character sum identities over a field of q elements, where q is a power of a prime ...
Research in Number Theory 2017 3:8
Published on: 3 April 2017
Erratum
Research in Number Theory 2017 3:15
Published on: 28 March 2017
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Research in Number Theory 2017 3:7
Published on: 14 March 2017
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Research in Number Theory 2017 3:5
Published on: 1 March 2017
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Research in Number Theory 2017 3:2
Published on: 14 February 2017
Erratum
Research in Number Theory 2017 3:12
Published on: 10 February 2017
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Research in Number Theory 2017 3:4
Published on: 1 February 2017
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We study the variance of sums of the indicator function of square-full polynomials in both arithmetic progressions and short intervals. Our work is in the context of the ring ...
Research in Number Theory 2017 3:3
Published on: 17 January 2017
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We prove an explicit formula for the polynomial part of a restricted partition function, also known as the first Sylvester wave. This is achieved by way of some identities for higher-order Bernoulli polynomial...
Research in Number Theory 2017 3:1
Published on: 5 January 2017
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Research in Number Theory 2016 2:34
Published on: 14 December 2016
Research
We revisit a statement of Birch that the field of moduli for a marked three-point ramified cover is a field of definition. Classical criteria due to Dèbes and Emsalem can be used to prove this statement in the...
Research in Number Theory 2016 2:27
Published on: 13 December 2016
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We generalize a result of Garvan on inequalities and interpretations of the moments of the partition rank and crank functions. In particular for nearly 30 Bailey pairs, we introduce a rank-like function, estab...
Research in Number Theory 2016 2:35
Published on: 13 December 2016