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A note about the generic irreducibility of the spectrum of the Laplacian on homogeneous spaces
Petrecca and Röser (Mathematische Zeitschrift 291:395–419, 2018) and Schueth (Ann Global Anal Geom 52:187–200, 2017) had shown that for a generic G -in...
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On near orthogonality of certain k-vectors involving generalized Ramanujan sums
The near orthgonality of certain k -vectors involving the Ramanujan sums were studied by Alkan (J Number Theory 140:147–168, 2014). Here we undertake...
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Étale cohomology of algebraizable rigid analytic varieties via nearby cycles over general bases
We prove a finiteness theorem and a comparison theorem in the theory of étale cohomology of rigid analytic varieties. By a result of Huber, for a...
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On a generalization of 5-dissections of some infinite q-products
In this paper, we prove 5-dissection formulas for a group of certain types of infinite products. Our approach provides unified proofs and extends the...
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Generalized Mahler measures of Laurent polynomials
Following the work of Lalín and Mittal on the Mahler measure over arbitrary tori, we investigate the definition of the generalized Mahler measure for...
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Exact formula for cubic partitions
We obtain an exact formula for the cubic partition function and prove a conjecture by Banerjee, Paule, Radu and Zeng.
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Deviation of the rank and crank modulo 11
In this paper, we build on the recent results of Frank Garvan and Rishabh Sarma as well as classical results of Bruce Berndt in order to establish...
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Singular contact varieties
In this note we propose the generalization of the notion of a holomorphic contact structure on a manifold (smooth variety) to varieties with rational...
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Arithmetic statistics for Galois deformation rings
Given an elliptic curve E defined over the rational numbers and a prime p at which E has good reduction, we consider the Galois deformation ring...
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